{"id":7144,"date":"2025-09-10T11:21:36","date_gmt":"2025-09-10T02:21:36","guid":{"rendered":"https:\/\/blog.since2020.jp\/?p=7144"},"modified":"2025-09-10T11:21:36","modified_gmt":"2025-09-10T02:21:36","slug":"stochastic_process","status":"publish","type":"post","link":"https:\/\/since2020.jp\/media\/stochastic_process\/","title":{"rendered":"\u78ba\u7387\u904e\u7a0b\u306e\u57fa\u790e"},"content":{"rendered":"\n<p>\u78ba\u7387\u904e\u7a0b\u306f\u3001\u6642\u9593\u7d4c\u904e\u306b\u4f34\u3063\u3066\u5909\u5316\u3059\u308b\u78ba\u7387\u73fe\u8c61\u3092\u6570\u5b66\u7684\u306b\u8a18\u8ff0\u3059\u308b\u3082\u306e\u3067\u3059\u3002\u91d1\u878d\u5e02\u5834\u306e\u4fa1\u683c\u5909\u52d5\u3001\u5f85\u3061\u884c\u5217\u30b7\u30b9\u30c6\u30e0\u306a\u3069\u3001\u79c1\u305f\u3061\u306e\u8eab\u306e\u56de\u308a\u306e\u591a\u304f\u306e\u73fe\u8c61\u304c\u78ba\u7387\u904e\u7a0b\u3068\u3057\u3066\u30e2\u30c7\u30eb\u5316\u3067\u304d\u307e\u3059\u3002\u4eca\u56de\u306f\u3001\u78ba\u7387\u904e\u7a0b\u306e\u57fa\u672c\u6982\u5ff5\u306e\u8aac\u660e\u304b\u3089\u59cb\u307e\u308a\u3001\u5b9f\u969b\u306bR\u3067\u5b9f\u88c5\u3059\u308b\u3068\u3053\u308d\u307e\u3067\u53d6\u308a\u7d44\u307f\u307e\u3059\u3002<\/p>\n\n\n<h2>\u78ba\u7387\u904e\u7a0b\u3068\u306f\u4f55\u304b<\/h2>\n<b>\u57fa\u672c\u5b9a\u7fa9<\/b>\r\n<p><strong>\u78ba\u7387\u904e\u7a0b<\/strong>\u3068\u306f\u3001\u6642\u9593 \\(t\\) \u3067\u30d1\u30e9\u30e1\u30fc\u30bf\u5316\u3055\u308c\u305f\u78ba\u7387\u5909\u6570\u306e\u65cf\u306e\u3053\u3068\u3067\u3059\u3002\u6570\u5b66\u7684\u306b\u306f\u6b21\u306e\u3088\u3046\u306b\u8868\u73fe\u3055\u308c\u307e\u3059\uff1a<\/p>\r\n<p>$$\\{X(t), t \\in T\\}$$<\/p>\r\n<p>\u3053\u3053\u3067\u3001\\(T\\) \u306f\u6642\u9593\u306e\u96c6\u5408\uff08\u30d1\u30e9\u30e1\u30fc\u30bf\u7a7a\u9593\uff09\u3001\\(X(t)\\) \u306f\u6642\u523b \\(t\\) \u306b\u304a\u3051\u308b\u78ba\u7387\u5909\u6570\u3067\u3059\u3002<\/p>\r\n<b>\u5206\u985e<\/b>\r\n<p>\u78ba\u7387\u904e\u7a0b\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5206\u985e\u3055\u308c\u307e\u3059\uff1a<\/p>\r\n<ul>\r\n\t<li><strong>\u6642\u9593\u306b\u3088\u308b\u5206\u985e<\/strong>\uff1a\r\n\r\n<ul>\r\n\t<li>\u96e2\u6563\u6642\u9593\u78ba\u7387\u904e\u7a0b\uff1a\\(T = \\{0, 1, 2, &#8230;\\}\\)<\/li>\r\n\t<li>\u9023\u7d9a\u6642\u9593\u78ba\u7387\u904e\u7a0b\uff1a\\(T = [0, \\infty)\\)<\/li>\r\n<\/ul>\r\n<\/li>\r\n\t<li><strong>\u72b6\u614b\u7a7a\u9593\u306b\u3088\u308b\u5206\u985e<\/strong>\uff1a\r\n\r\n<ul>\r\n\t<li>\u96e2\u6563\u72b6\u614b\uff1a\\(X(t) \\in \\{0, 1, 2, &#8230;\\}\\)<\/li>\r\n\t<li>\u9023\u7d9a\u72b6\u614b\uff1a\\(X(t) \\in \\mathbb{R}\\)<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\n\n<h2>\u30d6\u30e9\u30a6\u30f3\u904b\u52d5\uff08Brownian Motion\uff09<\/h2>\n<b>\u5b9a\u7fa9\u3068\u6027\u8cea<\/b>\r\n<p><strong>\u30d6\u30e9\u30a6\u30f3\u904b\u52d5<\/strong>\uff08\u307e\u305f\u306f\u30a6\u30a3\u30fc\u30ca\u30fc\u904e\u7a0b\uff09\u306f\u3001\u9023\u7d9a\u6642\u9593\u30fb\u9023\u7d9a\u72b6\u614b\u306e\u78ba\u7387\u904e\u7a0b\u3067\u3001\u4ee5\u4e0b\u306e\u6027\u8cea\u3092\u6e80\u305f\u3057\u307e\u3059\uff1a<\/p>\r\n<ol>\r\n\t<li><strong>\u521d\u671f\u6761\u4ef6<\/strong>\uff1a\\(W(0) = 0\\)<\/li>\r\n\t<li><strong>\u72ec\u7acb\u5897\u5206<\/strong>\uff1a\u4efb\u610f\u306e \\(0 \\leq t_1 &lt; t_2 \\leq t_3 &lt; t_4\\) \u306b\u5bfe\u3057\u3066\u3001\\(W(t_2) &#8211; W(t_1)\\) \u3068 \\(W(t_4) &#8211; W(t_3)\\) \u306f\u72ec\u7acb<\/li>\r\n\t<li><strong>\u6b63\u898f\u5206\u5e03<\/strong>\uff1a\u4efb\u610f\u306e \\(t &gt; 0\\) \u306b\u5bfe\u3057\u3066\u3001\\(W(t) \\sim N(0, \\sigma^2 t)\\)<\/li>\r\n\t<li><strong>\u9023\u7d9a\u8ecc\u9053<\/strong>\uff1a\\(W(t)\\) \u306f \\(t\\) \u306b\u95a2\u3057\u3066\u9023\u7d9a<\/li>\r\n<\/ol>\r\n<b>\u6570\u5b66\u7684\u8868\u73fe<\/b>\r\n<p>\u6a19\u6e96\u30d6\u30e9\u30a6\u30f3\u904b\u52d5\u3067\u306f \\(\\sigma = 1\\) \u3068\u3057\u3001\u4efb\u610f\u306e\u6642\u70b9 \\(t\\) \u3067\u306e\u5206\u5e03\u306f\uff1a<\/p>\r\n<p>$$W(t) \\sim N(0, t)$$<\/p>\r\n<p>\u307e\u305f\u3001\u5897\u5206\u306e\u6027\u8cea\u306f\uff1a<\/p>\r\n<p>$$W(t) &#8211; W(s) \\sim N(0, t-s) \\quad \\text{for } t &gt; s$$<\/p>\r\n<b>\u5fdc\u7528\u5206\u91ce<\/b>\r\n<ul>\r\n\t<li><strong>\u91d1\u878d\u5de5\u5b66<\/strong>\uff1a\u682a\u4fa1\u306e\u30e2\u30c7\u30eb\u5316\uff08\u5e7e\u4f55\u30d6\u30e9\u30a6\u30f3\u904b\u52d5\uff09<\/li>\r\n\t<li><strong>\u7269\u7406\u5b66<\/strong>\uff1a\u7c92\u5b50\u306e\u30e9\u30f3\u30c0\u30e0\u306a\u904b\u52d5<\/li>\r\n\t<li><strong>\u5de5\u5b66<\/strong>\uff1a\u30ce\u30a4\u30ba\u306e\u30e2\u30c7\u30eb\u5316<\/li>\r\n<\/ul>\n\n<h2>\u30dd\u30a2\u30bd\u30f3\u904e\u7a0b\uff08Poisson Process\uff09<\/h2>\n<b>\u5b9a\u7fa9\u3068\u6027\u8cea<\/b>\r\n<p><strong>\u30dd\u30a2\u30bd\u30f3\u904e\u7a0b<\/strong>\u306f\u3001\u96e2\u6563\u7684\u306a\u4e8b\u8c61\u306e\u767a\u751f\u3092\u30e2\u30c7\u30eb\u5316\u3059\u308b\u78ba\u7387\u904e\u7a0b\u3067\u3059\u3002\u30ec\u30fc\u30c8 \\(\\lambda\\) \u306e\u30dd\u30a2\u30bd\u30f3\u904e\u7a0b \\(\\{N(t), t \\geq 0\\}\\) \u306f\u4ee5\u4e0b\u306e\u6027\u8cea\u3092\u6e80\u305f\u3057\u307e\u3059\uff1a<\/p>\r\n<ol>\r\n\t<li><strong>\u521d\u671f\u6761\u4ef6<\/strong>\uff1a\\(N(0) = 0\\)<\/li>\r\n\t<li><strong>\u72ec\u7acb\u5897\u5206<\/strong>\uff1a\u91cd\u8907\u3057\u306a\u3044\u6642\u9593\u533a\u9593\u3067\u306e\u5897\u5206\u306f\u72ec\u7acb<\/li>\r\n\t<li><strong>\u5b9a\u5e38\u5897\u5206<\/strong>\uff1a\u5897\u5206\u306e\u5206\u5e03\u306f\u6642\u9593\u533a\u9593\u306e\u9577\u3055\u306e\u307f\u306b\u4f9d\u5b58<\/li>\r\n\t<li><strong>\u30dd\u30a2\u30bd\u30f3\u5206\u5e03<\/strong>\uff1a\u4efb\u610f\u306e \\(t &gt; 0\\) \u306b\u5bfe\u3057\u3066\u3001\\(N(t) \\sim \\text{Poisson}(\\lambda t)\\)<\/li>\r\n<\/ol>\r\n<b>\u6570\u5b66\u7684\u8868\u73fe<\/b>\r\n<p>\u6642\u523b \\(t\\) \u307e\u3067\u306e\u4e8b\u8c61\u767a\u751f\u56de\u6570\u306e\u5206\u5e03\uff1a<\/p>\r\n<p>$$P(N(t) = k) = \\frac{(\\lambda t)^k e^{-\\lambda t}}{k!}$$<\/p>\r\n<p>\u4e8b\u8c61\u9593\u9694\u306e\u5206\u5e03\uff08\u6307\u6570\u5206\u5e03\uff09\uff1a<\/p>\r\n<p>$$T_1, T_2, \\ldots \\sim \\text{Exp}(\\lambda)$$<\/p>\r\n<b>\u5fdc\u7528\u5206\u91ce<\/b>\r\n<ul>\r\n\t<li><strong>\u5f85\u3061\u884c\u5217\u7406\u8ad6<\/strong>\uff1a\u9867\u5ba2\u306e\u5230\u7740\u904e\u7a0b<\/li>\r\n\t<li><strong>\u4fe1\u983c\u6027\u5de5\u5b66<\/strong>\uff1a\u6545\u969c\u306e\u767a\u751f<\/li>\r\n\t<li><strong>\u75ab\u5b66<\/strong>\uff1a\u75c5\u6c17\u306e\u767a\u75c7<\/li>\r\n\t<li><strong>\u901a\u4fe1\u5de5\u5b66<\/strong>\uff1a\u30d1\u30b1\u30c3\u30c8\u306e\u5230\u7740<\/li>\r\n<\/ul>\n\n<h2>\u8907\u5408\u30dd\u30a2\u30bd\u30f3\u904e\u7a0b\uff08Compound Poisson Process\uff09<\/h2>\n<b>\u5b9a\u7fa9<\/b>\r\n<p><strong>\u8907\u5408\u30dd\u30a2\u30bd\u30f3\u904e\u7a0b<\/strong>\u306f\u3001\u30dd\u30a2\u30bd\u30f3\u904e\u7a0b\u306e\u5404\u4e8b\u8c61\u306b\u5bfe\u3057\u3066\u30e9\u30f3\u30c0\u30e0\u306a\u30b5\u30a4\u30ba\uff08\u30b8\u30e3\u30f3\u30d7\uff09\u3092\u5272\u308a\u5f53\u3066\u305f\u904e\u7a0b\u3067\u3059\uff1a<\/p>\r\n<p>$$S(t) = \\sum_{i=1}^{N(t)} Y_i$$<\/p>\r\n<p>\u3053\u3053\u3067\u3001\\(\\{N(t)\\}\\) \u306f\u30ec\u30fc\u30c8 \\(\\lambda\\) \u306e\u30dd\u30a2\u30bd\u30f3\u904e\u7a0b\u3001\\(\\{Y_i\\}\\) \u306f\u72ec\u7acb\u540c\u5206\u5e03\u306e\u30e9\u30f3\u30c0\u30e0\u5909\u6570\uff08\u30b8\u30e3\u30f3\u30d7\u30b5\u30a4\u30ba\uff09\u3067\u3059\u3002<\/p>\r\n<b>\u5fdc\u7528\u5206\u91ce<\/b>\r\n<ul>\r\n\t<li><strong>\u4fdd\u967a\u6570\u5b66<\/strong>\uff1a\u4fdd\u967a\u91d1\u8acb\u6c42\u306e\u7dcf\u984d<\/li>\r\n\t<li><strong>\u30ea\u30b9\u30af\u7406\u8ad6<\/strong>\uff1a\u640d\u5931\u306e\u7d2f\u7a4d\u30e2\u30c7\u30eb<\/li>\r\n\t<li><strong>\u5728\u5eab\u7ba1\u7406<\/strong>\uff1a\u9700\u8981\u306e\u30e2\u30c7\u30eb\u5316<\/li>\r\n<\/ul>\n\n<h2>\u78ba\u7387\u904e\u7a0b\u306e\u7d71\u8a08\u7684\u6027\u8cea\u306e\u89e3\u6790\uff1a\u30e2\u30fc\u30e1\u30f3\u30c8\u6cd5<\/h2>\n<p>\u3053\u3053\u307e\u3067\u78ba\u7387\u904e\u7a0b\u306e\u5b9a\u7fa9\u3068\u57fa\u672c\u7684\u306a\u6027\u8cea\u3092\u898b\u3066\u304d\u307e\u3057\u305f\u304c\u3001\u5b9f\u969b\u306e\u5fdc\u7528\u3067\u306f\u300c\u3053\u306e\u78ba\u7387\u904e\u7a0b\u304c\u7406\u8ad6\u901a\u308a\u306b\u632f\u308b\u821e\u3063\u3066\u3044\u308b\u304b\u300d\u3092\u691c\u8a3c\u3057\u305f\u308a\u3001\u300c\u7570\u306a\u308b\u78ba\u7387\u904e\u7a0b\u3092\u6bd4\u8f03\u3057\u305f\u308a\u300d\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\r\n<p>\u3057\u304b\u3057\u3001\u78ba\u7387\u904e\u7a0b\u306f\u7121\u9650\u6b21\u5143\u306e\u8907\u96d1\u306a\u5bfe\u8c61\u3067\u3042\u308a\u3001\u305d\u306e\u5168\u4f53\u7684\u306a\u6027\u8cea\u3092\u76f4\u63a5\u8abf\u3079\u308b\u3053\u3068\u306f\u56f0\u96e3\u3067\u3059\u3002\u305d\u3053\u3067\u767b\u5834\u3059\u308b\u306e\u304c<strong>\u30e2\u30fc\u30e1\u30f3\u30c8\u6cd5<\/strong>\u3067\u3059\u3002<\/p>\r\n<b>\u30e2\u30fc\u30e1\u30f3\u30c8\u6cd5\u3068\u306f\u4f55\u304b\u3001\u306a\u305c\u4f7f\u3046\u306e\u304b<\/b>\r\n<p><strong>\u30e2\u30fc\u30e1\u30f3\u30c8\u6cd5<\/strong>\u306f\u3001\u78ba\u7387\u904e\u7a0b\u306e\u8907\u96d1\u306a\u6027\u8cea\u3092\u3001\u5e73\u5747\uff081\u6b21\u30e2\u30fc\u30e1\u30f3\u30c8\uff09\u3001\u5206\u6563\uff082\u6b21\u4e2d\u5fc3\u30e2\u30fc\u30e1\u30f3\u30c8\uff09\u3001\u5171\u5206\u6563\u306a\u3069\u306e\u300c\u8981\u7d04\u7d71\u8a08\u91cf\u300d\u3092\u901a\u3058\u3066\u8abf\u3079\u308b\u624b\u6cd5\u3067\u3059\u3002<\/p>\r\n<p>\u30e2\u30fc\u30e1\u30f3\u30c8\u6cd5\u304c\u91cd\u8981\u306a\u7406\u7531\uff1a<\/p>\r\n<ol>\r\n\t<li><strong>\u8a08\u7b97\u306e\u7c21\u4fbf\u6027<\/strong>\uff1a\u7121\u9650\u6b21\u5143\u306e\u78ba\u7387\u904e\u7a0b\u3092\u6709\u9650\u500b\u306e\u6570\u5024\u3067\u7279\u5fb4\u3065\u3051\u3067\u304d\u308b<\/li>\r\n\t<li><strong>\u7406\u8ad6\u3068\u5b9f\u8df5\u306e\u6a4b\u6e21\u3057<\/strong>\uff1a\u7406\u8ad6\u7684\u306a\u6027\u8cea\u3092\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3067\u691c\u8a3c\u3067\u304d\u308b<\/li>\r\n\t<li><strong>\u30e2\u30c7\u30eb\u9078\u629e\u306e\u6307\u91dd<\/strong>\uff1a\u89b3\u6e2c\u30c7\u30fc\u30bf\u304c\u3069\u306e\u78ba\u7387\u904e\u7a0b\u306b\u5f93\u3046\u304b\u3092\u5224\u65ad\u3067\u304d\u308b<\/li>\r\n\t<li><strong>\u30d1\u30e9\u30e1\u30fc\u30bf\u63a8\u5b9a<\/strong>\uff1a\u5b9f\u30c7\u30fc\u30bf\u304b\u3089\u78ba\u7387\u904e\u7a0b\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u63a8\u5b9a\u3067\u304d\u308b<\/li>\r\n<\/ol>\r\n<p>\u4f8b\u3048\u3070\u3001\u91d1\u878d\u30c7\u30fc\u30bf\u304c\u672c\u5f53\u306b\u30d6\u30e9\u30a6\u30f3\u904b\u52d5\u306b\u5f93\u3046\u304b\u3092\u8abf\u3079\u308b\u969b\u3001\u5168\u3066\u306e\u8ecc\u9053\u3092\u6bd4\u8f03\u3059\u308b\u306e\u306f\u4e0d\u53ef\u80fd\u3067\u3059\u304c\u3001\u5e73\u5747\u3084\u5206\u6563\u306e\u6642\u9593\u4f9d\u5b58\u6027\u3092\u8abf\u3079\u308b\u3053\u3068\u3067\u691c\u8a3c\u3067\u304d\u307e\u3059\u3002<\/p>\r\n<b>\u30e2\u30fc\u30e1\u30f3\u30c8\u6cd5\u306b\u3088\u308b\u5177\u4f53\u7684\u89e3\u6790<\/b>\r\n<b>\u30d6\u30e9\u30a6\u30f3\u904b\u52d5\u306e\u30e2\u30fc\u30e1\u30f3\u30c8<\/b>\r\n<p>\u6a19\u6e96\u30d6\u30e9\u30a6\u30f3\u904b\u52d5 \\(W(t)\\) \u306b\u3064\u3044\u3066\uff1a<\/p>\r\n<ul>\r\n\t<li><strong>\u5e73\u5747\u95a2\u6570<\/strong>\uff1a\\(m(t) = E[W(t)] = 0\\)<\/li>\r\n\t<li><strong>\u5206\u6563\u95a2\u6570<\/strong>\uff1a\\(\\text{Var}[W(t)] = t\\)<\/li>\r\n\t<li><strong>\u5171\u5206\u6563\u95a2\u6570<\/strong>\uff1a\\(\\text{Cov}[W(s), W(t)] = \\min(s, t)\\)<\/li>\r\n<\/ul>\r\n<p>\u3053\u308c\u3089\u306e\u6027\u8cea\u306b\u3088\u308a\u3001\u30d6\u30e9\u30a6\u30f3\u904b\u52d5\u3067\u306f\uff1a<\/p>\r\n<ul>\r\n\t<li>\u5e73\u5747\u306f\u6642\u9593\u306b\u3088\u3089\u305a0\u3092\u4fdd\u3064<\/li>\r\n\t<li>\u5206\u6563\u306f\u6642\u9593\u306b\u6bd4\u4f8b\u3057\u3066\u5897\u52a0\u3059\u308b<\/li>\r\n\t<li>\u7570\u306a\u308b\u6642\u70b9\u3067\u306e\u5024\u306b\u306f\u76f8\u95a2\u304c\u3042\u308b<\/li>\r\n<\/ul>\r\n<b>\u30dd\u30a2\u30bd\u30f3\u904e\u7a0b\u306e\u30e2\u30fc\u30e1\u30f3\u30c8<\/b>\r\n<p>\u30ec\u30fc\u30c8 \\(\\lambda\\) \u306e\u30dd\u30a2\u30bd\u30f3\u904e\u7a0b \\(N(t)\\) \u306b\u3064\u3044\u3066\uff1a<\/p>\r\n<ul>\r\n\t<li><strong>\u5e73\u5747\u95a2\u6570<\/strong>\uff1a\\(E[N(t)] = \\lambda t\\)<\/li>\r\n\t<li><strong>\u5206\u6563\u95a2\u6570<\/strong>\uff1a\\(\\text{Var}[N(t)] = \\lambda t\\)<\/li>\r\n\t<li><strong>\u5171\u5206\u6563\u95a2\u6570<\/strong>\uff1a\\(\\text{Cov}[N(s), N(t)] = \\lambda \\min(s, t)\\)<\/li>\r\n<\/ul>\r\n<p>\u30dd\u30a2\u30bd\u30f3\u904e\u7a0b\u3067\u306f\uff1a<\/p>\r\n<ul>\r\n\t<li>\u5e73\u5747\u3068\u5206\u6563\u304c\u7b49\u3057\u304f\u3001\u3069\u3061\u3089\u3082\u6642\u9593\u306b\u6bd4\u4f8b<\/li>\r\n\t<li>\u3053\u306e\u6027\u8cea\u3092\u5229\u7528\u3057\u3066\u30ec\u30fc\u30c8\u30d1\u30e9\u30e1\u30fc\u30bf \\(\\lambda\\) \u3092\u63a8\u5b9a\u3067\u304d\u308b<\/li>\r\n<\/ul>\r\n<b>\u8907\u5408\u30dd\u30a2\u30bd\u30f3\u904e\u7a0b\u306e\u30e2\u30fc\u30e1\u30f3\u30c8<\/b>\r\n<p>\\(Y_i\\) \u306e\u5e73\u5747\u3092 \\(\\mu\\)\u3001\u5206\u6563\u3092 \\(\\sigma^2\\) \u3068\u3059\u308b\u3068\uff1a<\/p>\r\n<ul>\r\n\t<li><strong>\u5e73\u5747<\/strong>\uff1a\\(E[S(t)] = \\lambda t \\mu\\)<\/li>\r\n\t<li><strong>\u5206\u6563<\/strong>\uff1a\\(\\text{Var}[S(t)] = \\lambda t E[Y^2]\\)<\/li>\r\n<\/ul>\r\n<p>\u3053\u308c\u306b\u3088\u308a\u3001\u30b8\u30e3\u30f3\u30d7\u306e\u767a\u751f\u983b\u5ea6\u3068\u30b5\u30a4\u30ba\u3092\u5206\u96e2\u3057\u3066\u5206\u6790\u3067\u304d\u307e\u3059\u3002<\/p>\n\n<h2>R\u306b\u3088\u308b\u5b9f\u88c5\u3068\u691c\u8a3c<\/h2>\n<p>\u305d\u308c\u3067\u306f\u30013\u3064\u306e\u78ba\u7387\u904e\u7a0b\u306b\u3064\u3044\u3066\u3001\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3067\u7406\u8ad6\u5024\u3068\u5b9f\u6e2c\u5024\u3092\u6bd4\u8f03\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002<!-- notionvc: 203a5925-64cc-4af4-a5c6-22868faa532d --><\/p>\r\n<b>\u30d6\u30e9\u30a6\u30f3\u904b\u52d5\u306e\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3<\/b>\r\n<pre><code class=\"language-r\"><\/code><\/pre>\r\n<div class=\"hcb_wrap\">\r\n<pre class=\"prism line-numbers lang-python\" data-lang=\"Python\"><code># Required libraries\r\nlibrary(ggplot2)\r\nlibrary(dplyr)\r\n\r\n# Brownian Motion Simulation\r\nsimulate_brownian_motion &lt;- function(n_steps = 1000, dt = 0.01, sigma = 1) {\r\n  # Time grid\r\n  t &lt;- seq(0, n_steps * dt, by = dt)\r\n\r\n  # Generate increments (normally distributed)\r\n  dW &lt;- rnorm(n_steps, mean = 0, sd = sqrt(dt))\r\n\r\n  # Cumulative sum to get Brownian motion path\r\n  W &lt;- c(0, cumsum(dW))\r\n\r\n  # Return data frame\r\n  data.frame(\r\n    time = t,\r\n    value = W * sigma\r\n  )\r\n}\r\n\r\n# Generate multiple paths\r\nset.seed(123)\r\nn_paths &lt;- 5\r\nbrownian_paths &lt;- list()\r\n\r\nfor(i in 1:n_paths) {\r\n  brownian_paths[[i]] &lt;- simulate_brownian_motion(n_steps = 1000, dt = 0.01)\r\n  brownian_paths[[i]]$path &lt;- paste(\"Path\", i)\r\n}\r\n\r\n# Combine all paths\r\nbrownian_data &lt;- do.call(rbind, brownian_paths)\r\n\r\n# Visualization\r\np1 &lt;- ggplot(brownian_data, aes(x = time, y = value, color = path)) +\r\n  geom_line(alpha = 0.8, size = 0.7) +\r\n  labs(title = \"Brownian Motion Simulation\",\r\n       subtitle = \"Multiple sample paths\",\r\n       x = \"Time\",\r\n       y = \"W(t)\",\r\n       color = \"Sample Path\") +\r\n  theme_minimal() +\r\n  theme(plot.title = element_text(size = 16, face = \"bold\"),\r\n        axis.title = element_text(size = 12, face = \"bold\"))\r\n\r\nprint(p1)\r\n\r\n# Statistical properties verification using moment method\r\nfinal_time &lt;- max(brownian_data$time)\r\nfinal_values &lt;- brownian_data[brownian_data$time == final_time, \"value\"]\r\n\r\ncat(\"=== Brownian Motion Properties (Moment Method Verification) ===\\\\n\")\r\ncat(\"Theoretical mean at t =\", final_time, \": 0\\\\n\")\r\ncat(\"Empirical mean:\", round(mean(final_values), 3), \"\\\\n\")\r\ncat(\"Theoretical variance at t =\", final_time, \":\", final_time, \"\\\\n\")\r\ncat(\"Empirical variance:\", round(var(final_values), 3), \"\\\\n\")\r\ncat(\"Theory matches empirical results:\",\r\n    abs(mean(final_values)) &lt; 0.5 &amp;&amp; abs(var(final_values) - final_time) &lt; 0.5, \"\\\\n\")<\/code><\/pre>\r\n<\/div>\r\n<pre>\u51fa\u529b\u7d50\u679c<\/pre>\r\n<div class=\"hcb_wrap\">\r\n<pre class=\"prism line-numbers lang-plain\" data-lang=\"Plain Text\"><code>=== Brownian Motion Properties (Moment Method Verification) ===\r\nTheoretical mean at t = 10 : 0\r\nEmpirical mean: 1.613 \r\nTheoretical variance at t = 10 : 10 \r\nEmpirical variance: NA \r\nTheory matches empirical results: FALSE<\/code><\/pre>\r\n<\/div>\r\n<p><img decoding=\"async\" src=\"https:\/\/since2020.jp\/media\/wp-content\/uploads\/2025\/09\/brownian_motion.png\" alt=\"\" width=\"428\" height=\"423\" class=\"size-full wp-image-7147 aligncenter\" srcset=\"https:\/\/since2020.jp\/media\/wp-content\/uploads\/2025\/09\/brownian_motion.png 428w, https:\/\/since2020.jp\/media\/wp-content\/uploads\/2025\/09\/brownian_motion-300x296.png 300w, https:\/\/since2020.jp\/media\/wp-content\/uploads\/2025\/09\/brownian_motion-120x120.png 120w\" sizes=\"(max-width: 428px) 100vw, 428px\" \/><\/p>\r\n<b>\u30dd\u30a2\u30bd\u30f3\u904e\u7a0b\u306e\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3<\/b>\r\n<div class=\"hcb_wrap\">\r\n<pre class=\"prism line-numbers lang-python\" data-lang=\"Python\"><code># Poisson Process Simulation\r\nsimulate_poisson_process &lt;- function(lambda = 1, T = 10) {\r\n  # Generate inter-arrival times (exponentially distributed)\r\n  times &lt;- c()\r\n  current_time &lt;- 0\r\n\r\n  while(current_time &lt; T) {\r\n    # Next inter-arrival time\r\n    inter_arrival &lt;- rexp(1, rate = lambda)\r\n    current_time &lt;- current_time + inter_arrival\r\n\r\n    if(current_time &lt;= T) {\r\n      times &lt;- c(times, current_time)\r\n    }\r\n  }\r\n\r\n  # Create counting process\r\n  if(length(times) == 0) {\r\n    return(data.frame(time = c(0, T), count = c(0, 0)))\r\n  }\r\n\r\n  # Add initial and final points\r\n  all_times &lt;- c(0, times, T)\r\n  counts &lt;- c(0, 1:length(times), length(times))\r\n\r\n  return(data.frame(time = all_times, count = counts))\r\n}\r\n\r\n# Generate multiple realizations\r\nset.seed(456)\r\nlambda &lt;- 2  # Rate parameter\r\nT_max &lt;- 5   # Time horizon\r\nn_realizations &lt;- 3\r\n\r\npoisson_paths &lt;- list()\r\nfor(i in 1:n_realizations) {\r\n  poisson_paths[[i]] &lt;- simulate_poisson_process(lambda = lambda, T = T_max)\r\n  poisson_paths[[i]]$realization &lt;- paste(\"Realization\", i)\r\n}\r\n\r\n# Combine data\r\npoisson_data &lt;- do.call(rbind, poisson_paths)\r\n\r\n# Visualization\r\np2 &lt;- ggplot(poisson_data, aes(x = time, y = count, color = realization)) +\r\n  geom_step(size = 1, alpha = 0.8) +\r\n  geom_point(size = 2, alpha = 0.8) +\r\n  labs(title = \"Poisson Process Simulation\",\r\n       subtitle = paste(\"Rate \u03bb =\", lambda),\r\n       x = \"Time\",\r\n       y = \"N(t) - Number of Events\",\r\n       color = \"Realization\") +\r\n  theme_minimal() +\r\n  theme(plot.title = element_text(size = 16, face = \"bold\"),\r\n        axis.title = element_text(size = 12, face = \"bold\"))\r\n\r\nprint(p2)\r\n\r\n# Moment method verification\r\ntheoretical_mean &lt;- lambda * T_max\r\nempirical_counts &lt;- poisson_data[poisson_data$time == T_max, \"count\"]\r\n\r\ncat(\"\\\\n=== Poisson Process Properties (Moment Method Verification) ===\\\\n\")\r\ncat(\"Time horizon T =\", T_max, \"\\\\n\")\r\ncat(\"Rate \u03bb =\", lambda, \"\\\\n\")\r\ncat(\"Theoretical mean N(T):\", theoretical_mean, \"\\\\n\")\r\ncat(\"Empirical mean:\", round(mean(empirical_counts), 3), \"\\\\n\")\r\ncat(\"Theoretical variance:\", theoretical_mean, \"\\\\n\")\r\ncat(\"Empirical variance:\", round(var(empirical_counts), 3), \"\\\\n\")\r\n\r\n# Inter-arrival times analysis (additional moment method application)\r\nall_arrivals &lt;- c()\r\nfor(i in 1:n_realizations) {\r\n  path_data &lt;- poisson_paths[[i]]\r\n  arrivals &lt;- path_data$time[path_data$time &gt; 0 &amp; path_data$time &lt; T_max]\r\n  if(length(arrivals) &gt; 1) {\r\n    inter_arrivals &lt;- diff(c(0, arrivals))\r\n    all_arrivals &lt;- c(all_arrivals, inter_arrivals)\r\n  }\r\n}\r\n\r\nif(length(all_arrivals) &gt; 0) {\r\n  cat(\"\\\\n=== Inter-arrival Times (Exponential Distribution Check) ===\\\\n\")\r\n  cat(\"Theoretical mean (1\/\u03bb):\", 1\/lambda, \"\\\\n\")\r\n  cat(\"Empirical mean:\", round(mean(all_arrivals), 3), \"\\\\n\")\r\n  cat(\"Number of inter-arrivals:\", length(all_arrivals), \"\\\\n\")\r\n  cat(\"Distribution check passed:\", abs(mean(all_arrivals) - 1\/lambda) &lt; 0.2, \"\\\\n\")\r\n}\r\n<\/code><\/pre>\r\n<\/div>\r\n<pre>\u51fa\u529b\u7d50\u679c<\/pre>\r\n<div class=\"hcb_wrap\">\r\n<pre class=\"prism line-numbers lang-plain\" data-lang=\"Plain Text\"><code>=== Brownian Motion Properties (Moment Method Verification) ===\r\nTheoretical mean at t = 10 : 0\r\nEmpirical mean: 1.613 \r\nTheoretical variance at t = 10 : 10 \r\nEmpirical variance: NA \r\nTheory matches empirical results: FALSE<\/code><\/pre>\r\n<\/div>\r\n<b><img decoding=\"async\" src=\"https:\/\/since2020.jp\/media\/wp-content\/uploads\/2025\/09\/poisson_process.png\" alt=\"\" width=\"425\" height=\"422\" class=\"alignnone size-full wp-image-7148 aligncenter\" srcset=\"https:\/\/since2020.jp\/media\/wp-content\/uploads\/2025\/09\/poisson_process.png 425w, https:\/\/since2020.jp\/media\/wp-content\/uploads\/2025\/09\/poisson_process-300x298.png 300w, https:\/\/since2020.jp\/media\/wp-content\/uploads\/2025\/09\/poisson_process-150x150.png 150w, https:\/\/since2020.jp\/media\/wp-content\/uploads\/2025\/09\/poisson_process-120x120.png 120w\" sizes=\"(max-width: 425px) 100vw, 425px\" \/><\/b>\r\n<b>\u8907\u5408\u30dd\u30a2\u30bd\u30f3\u904e\u7a0b\u306e\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3<\/b>\r\n<div class=\"hcb_wrap\">\r\n<pre class=\"prism line-numbers lang-python\" data-lang=\"Python\"><code># Compound Poisson Process Simulation\r\nsimulate_compound_poisson &lt;- function(lambda = 1, T = 10, jump_mean = 1, jump_sd = 0.5) {\r\n  # First, generate the underlying Poisson process\r\n  poisson_times &lt;- c()\r\n  current_time &lt;- 0\r\n\r\n  while(current_time &lt; T) {\r\n    inter_arrival &lt;- rexp(1, rate = lambda)\r\n    current_time &lt;- current_time + inter_arrival\r\n\r\n    if(current_time &lt;= T) {\r\n      poisson_times &lt;- c(poisson_times, current_time)\r\n    }\r\n  }\r\n\r\n  # If no events occurred\r\n  if(length(poisson_times) == 0) {\r\n    return(data.frame(\r\n      time = c(0, T),\r\n      value = c(0, 0),\r\n      jump_count = c(0, 0)\r\n    ))\r\n  }\r\n\r\n  # Generate jump sizes (assuming normal distribution for simplicity)\r\n  jump_sizes &lt;- rnorm(length(poisson_times), mean = jump_mean, sd = jump_sd)\r\n\r\n  # Create compound process values\r\n  times &lt;- c(0, poisson_times, T)\r\n  cumulative_jumps &lt;- c(0, cumsum(jump_sizes), sum(jump_sizes))\r\n  jump_counts &lt;- c(0, 1:length(poisson_times), length(poisson_times))\r\n\r\n  return(data.frame(\r\n    time = times,\r\n    value = cumulative_jumps,\r\n    jump_count = jump_counts,\r\n    stringsAsFactors = FALSE\r\n  ))\r\n}\r\n\r\n# Generate multiple compound Poisson realizations\r\nset.seed(789)\r\nlambda_compound &lt;- 1.5  # Jump rate\r\nT_max_compound &lt;- 8     # Time horizon\r\njump_mean &lt;- 2          # Mean jump size\r\njump_sd &lt;- 1            # Jump size standard deviation\r\nn_realizations_compound &lt;- 4\r\n\r\ncompound_paths &lt;- list()\r\nfor(i in 1:n_realizations_compound) {\r\n  compound_paths[[i]] &lt;- simulate_compound_poisson(\r\n    lambda = lambda_compound,\r\n    T = T_max_compound,\r\n    jump_mean = jump_mean,\r\n    jump_sd = jump_sd\r\n  )\r\n  compound_paths[[i]]$realization &lt;- paste(\"Realization\", i)\r\n}\r\n\r\n# Combine data\r\ncompound_data &lt;- do.call(rbind, compound_paths)\r\n\r\n# Visualization\r\np3 &lt;- ggplot(compound_data, aes(x = time, y = value, color = realization)) +\r\n  geom_step(size = 1, alpha = 0.8) +\r\n  geom_point(size = 2, alpha = 0.8) +\r\n  labs(title = \"Compound Poisson Process Simulation\",\r\n       subtitle = paste(\"Rate \u03bb =\", lambda_compound, \", Jump Mean =\", jump_mean),\r\n       x = \"Time\",\r\n       y = \"S(t) - Cumulative Value\",\r\n       color = \"Realization\") +\r\n  theme_minimal() +\r\n  theme(plot.title = element_text(size = 16, face = \"bold\"),\r\n        axis.title = element_text(size = 12, face = \"bold\"))\r\n\r\nprint(p3)\r\n\r\n# Moment method verification for compound Poisson process\r\nfinal_values_compound &lt;- compound_data[compound_data$time == T_max_compound, \"value\"]\r\nfinal_counts_compound &lt;- compound_data[compound_data$time == T_max_compound, \"jump_count\"]\r\n\r\n# Theoretical moments\r\ntheoretical_mean_compound &lt;- lambda_compound * T_max_compound * jump_mean\r\ntheoretical_var_compound &lt;- lambda_compound * T_max_compound * (jump_sd^2 + jump_mean^2)\r\n\r\ncat(\"\\\\n=== Compound Poisson Process Properties (Moment Method Verification) ===\\\\n\")\r\ncat(\"Time horizon T =\", T_max_compound, \"\\\\n\")\r\ncat(\"Jump rate \u03bb =\", lambda_compound, \"\\\\n\")\r\ncat(\"Jump mean \u03bc =\", jump_mean, \"\\\\n\")\r\ncat(\"Jump variance \u03c3\u00b2 =\", jump_sd^2, \"\\\\n\")\r\n\r\ncat(\"\\\\n--- Process Values S(T) ---\\\\n\")\r\ncat(\"Theoretical mean E[S(T)] = \u03bbT\u03bc:\", round(theoretical_mean_compound, 3), \"\\\\n\")\r\ncat(\"Empirical mean:\", round(mean(final_values_compound), 3), \"\\\\n\")\r\ncat(\"Theoretical variance Var[S(T)] = \u03bbT(\u03c3\u00b2+\u03bc\u00b2):\", round(theoretical_var_compound, 3), \"\\\\n\")\r\ncat(\"Empirical variance:\", round(var(final_values_compound), 3), \"\\\\n\")\r\n\r\ncat(\"\\\\n--- Jump Counts N(T) ---\\\\n\")\r\ncat(\"Theoretical mean E[N(T)] = \u03bbT:\", lambda_compound * T_max_compound, \"\\\\n\")\r\ncat(\"Empirical mean:\", round(mean(final_counts_compound), 3), \"\\\\n\")\r\n\r\n# Extract all jump sizes for analysis\r\nall_jumps &lt;- c()\r\nfor(i in 1:n_realizations_compound) {\r\n  path_data &lt;- compound_paths[[i]]\r\n  if(nrow(path_data) &gt; 2) {  # More than just start and end points\r\n    jumps &lt;- diff(path_data$value[path_data$value != path_data$value[1]])\r\n    if(length(jumps) &gt; 0) {\r\n      # Remove zero differences (same values at consecutive time points)\r\n      jumps &lt;- jumps[jumps != 0]\r\n      all_jumps &lt;- c(all_jumps, jumps)\r\n    }\r\n  }\r\n}\r\n\r\nif(length(all_jumps) &gt; 0) {\r\n  cat(\"\\\\n--- Jump Sizes Analysis ---\\\\n\")\r\n  cat(\"Theoretical jump mean:\", jump_mean, \"\\\\n\")\r\n  cat(\"Empirical jump mean:\", round(mean(all_jumps), 3), \"\\\\n\")\r\n  cat(\"Theoretical jump variance:\", jump_sd^2, \"\\\\n\")\r\n  cat(\"Empirical jump variance:\", round(var(all_jumps), 3), \"\\\\n\")\r\n  cat(\"Number of observed jumps:\", length(all_jumps), \"\\\\n\")\r\n\r\n  # Check if moments match theory\r\n  mean_check &lt;- abs(mean(all_jumps) - jump_mean) &lt; 0.5\r\n  var_check &lt;- abs(var(all_jumps) - jump_sd^2) &lt; 1.0\r\n  cat(\"Jump distribution check passed:\", mean_check &amp;&amp; var_check, \"\\\\n\")\r\n}\r\n\r\n# Demonstrate the relationship between compound and simple Poisson processes\r\ncat(\"\\\\n=== Compound vs Simple Poisson Process ===\\\\n\")\r\ncat(\"When jump sizes = 1, compound Poisson reduces to simple Poisson\\\\n\")\r\n\r\n# Simulate compound Poisson with unit jumps\r\nunit_compound &lt;- simulate_compound_poisson(\r\n  lambda = lambda_compound,\r\n  T = T_max_compound,\r\n  jump_mean = 1,\r\n  jump_sd = 0  # No variance, all jumps = 1\r\n)\r\n\r\ncat(\"Unit jump compound process final value:\",\r\n    unit_compound$value[nrow(unit_compound)], \"\\\\n\")\r\ncat(\"Unit jump compound process final count:\",\r\n    unit_compound$jump_count[nrow(unit_compound)], \"\\\\n\")\r\ncat(\"These should be equal (and they are:\",\r\n    unit_compound$value[nrow(unit_compound)] == unit_compound$jump_count[nrow(unit_compound)], \")\\\\n\")<\/code><\/pre>\r\n<\/div>\r\n<pre><strong>\u51fa\u529b\u7d50\u679c<\/strong><\/pre>\r\n<div class=\"hcb_wrap\">\r\n<pre>=== Compound Poisson Process Properties (Moment Method Verification) ===\r\nTime horizon T = 8 \r\nJump rate \u03bb = 1.5 \r\nJump mean \u03bc = 2 \r\nJump variance \u03c3\u00b2 = 1 \r\n\r\n--- Process Values S(T) ---\r\nTheoretical mean E[S(T)] = \u03bbT\u03bc: 24 \r\nEmpirical mean: 14.371 \r\nTheoretical variance Var[S(T)] = \u03bbT(\u03c3\u00b2+\u03bc\u00b2): 60 \r\nEmpirical variance: NA \r\n\r\n--- Jump Counts N(T) ---\r\nTheoretical mean E[N(T)] = \u03bbT: 12 \r\nEmpirical mean: 9 \r\n\r\n--- Jump Sizes Analysis ---\r\nTheoretical jump mean: 2 \r\nEmpirical jump mean: 1.557 \r\nTheoretical jump variance: 1 \r\nEmpirical jump variance: 0.672 \r\nNumber of observed jumps: 8 \r\nJump distribution check passed: TRUE \r\n\r\n=== Compound vs Simple Poisson Process ===\r\nWhen jump sizes = 1, compound Poisson reduces to simple Poisson\r\nUnit jump compound process final value: 11 \r\nUnit jump compound process final count: 11 \r\nThese should be equal (and they are: TRUE )<\/pre>\r\n<\/div>\r\n<p><img decoding=\"async\" src=\"https:\/\/since2020.jp\/media\/wp-content\/uploads\/2025\/09\/compound_poisson_process.png\" alt=\"\" width=\"420\" height=\"420\" class=\"alignnone size-full wp-image-7149 aligncenter\" srcset=\"https:\/\/since2020.jp\/media\/wp-content\/uploads\/2025\/09\/compound_poisson_process.png 420w, https:\/\/since2020.jp\/media\/wp-content\/uploads\/2025\/09\/compound_poisson_process-300x300.png 300w, https:\/\/since2020.jp\/media\/wp-content\/uploads\/2025\/09\/compound_poisson_process-150x150.png 150w, https:\/\/since2020.jp\/media\/wp-content\/uploads\/2025\/09\/compound_poisson_process-120x120.png 120w\" sizes=\"(max-width: 420px) 100vw, 420px\" \/><\/p>\r\n<p><!-- notionvc: eacccd80-09ce-43b8-9338-8c2d659ae9c7 --><\/p>\n\n<h2>\u307e\u3068\u3081<\/h2>\n<p>\u78ba\u7387\u904e\u7a0b\u306f\u3001\u6642\u9593\u3068\u3068\u3082\u306b\u5909\u5316\u3059\u308b\u30e9\u30f3\u30c0\u30e0\u306a\u73fe\u8c61\u3092\u8a18\u8ff0\u3059\u308b\u5f37\u529b\u306a\u6570\u5b66\u7684\u67a0\u7d44\u307f\u3067\u3059\u3002\u4eca\u56de\u5b66\u3093\u3060\u5185\u5bb9\u3092\u307e\u3068\u3081\u308b\u3068\uff1a<\/p>\r\n<ul>\r\n\t<li><strong>\u30d6\u30e9\u30a6\u30f3\u904b\u52d5<\/strong>\u306f\u9023\u7d9a\u7684\u3067\u6b63\u898f\u5206\u5e03\u306b\u5f93\u3046\u904e\u7a0b\u3067\u3001\u91d1\u878d\u3084\u7269\u7406\u5b66\u3067\u306e\u5fdc\u7528\u304c\u5e83\u3044<\/li>\r\n\t<li><strong>\u30dd\u30a2\u30bd\u30f3\u904e\u7a0b<\/strong>\u306f\u96e2\u6563\u7684\u4e8b\u8c61\u306e\u767a\u751f\u3092\u30e2\u30c7\u30eb\u5316\u3057\u3001\u5f85\u3061\u884c\u5217\u3084\u4fe1\u983c\u6027\u306e\u5206\u91ce\u3067\u91cd\u8981<\/li>\r\n\t<li><strong>\u8907\u5408\u30dd\u30a2\u30bd\u30f3\u904e\u7a0b<\/strong>\u306f\u4e8b\u8c61\u306b\u30e9\u30f3\u30c0\u30e0\u306a\u30b5\u30a4\u30ba\u3092\u52a0\u3048\u305f\u3082\u306e\u3067\u3001\u4fdd\u967a\u3084\u30ea\u30b9\u30af\u7ba1\u7406\u3067\u6d3b\u7528\u3055\u308c\u308b<\/li>\r\n\t<li><strong>\u30e2\u30fc\u30e1\u30f3\u30c8\u6cd5<\/strong>\u306b\u3088\u308a\u3001\u8907\u96d1\u306a\u78ba\u7387\u904e\u7a0b\u306e\u6027\u8cea\u3092\u7c21\u6f54\u306b\u8981\u7d04\u3057\u3001\u7406\u8ad6\u3068\u5b9f\u8df5\u3092\u7d50\u3073\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u308b<\/li>\r\n<\/ul>\r\n<p>\u30e2\u30fc\u30e1\u30f3\u30c8\u6cd5\u306f\u3001\u78ba\u7387\u904e\u7a0b\u306e\u300c\u6307\u7d0b\u300d\u306e\u3088\u3046\u306a\u5f79\u5272\u3092\u679c\u305f\u3057\u307e\u3059\u3002\u5e73\u5747\u3001\u5206\u6563\u3001\u5171\u5206\u6563\u3068\u3044\u3046\u30b7\u30f3\u30d7\u30eb\u306a\u7d71\u8a08\u91cf\u3092\u901a\u3058\u3066\u3001\u7570\u306a\u308b\u78ba\u7387\u904e\u7a0b\u3092\u533a\u5225\u3057\u3001\u7406\u8ad6\u7684\u4e88\u6e2c\u3092\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3067\u691c\u8a3c\u3057\u3001\u5b9f\u30c7\u30fc\u30bf\u304b\u3089\u9069\u5207\u306a\u30e2\u30c7\u30eb\u3092\u9078\u629e\u3059\u308b\u3053\u3068\u304c\u53ef\u80fd\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\r\n<p>R\u306b\u3088\u308b\u5b9f\u88c5\u3092\u901a\u3058\u3066\u3001\u7406\u8ad6\u3068\u5b9f\u8df5\u3092\u7d50\u3073\u3064\u3051\u308b\u3053\u3068\u3067\u3001\u78ba\u7387\u904e\u7a0b\u306e\u7406\u89e3\u304c\u6df1\u307e\u308a\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u57fa\u790e\u77e5\u8b58\u306f\u3001\u3088\u308a\u9ad8\u5ea6\u306a\u78ba\u7387\u89e3\u6790\u3001\u91d1\u878d\u5de5\u5b66\u3001\u6a5f\u68b0\u5b66\u7fd2\u306e\u5206\u91ce\u3078\u306e\u767a\u5c55\u7684\u306a\u5b66\u7fd2\u306b\u3064\u306a\u304c\u308a\u307e\u3059\u3002<\/p>\r\n<p>\u78ba\u7387\u904e\u7a0b\u306e\u4e16\u754c\u306f\u5965\u304c\u6df1\u304f\u3001\u30de\u30eb\u30b3\u30d5\u904e\u7a0b\u3001\u30de\u30eb\u30c1\u30f3\u30b2\u30fc\u30eb\u3001\u78ba\u7387\u5fae\u5206\u65b9\u7a0b\u5f0f\u306a\u3069\u3001\u3055\u3089\u306b\u8c4a\u304b\u306a\u7406\u8ad6\u304c\u5f85\u3063\u3066\u3044\u307e\u3059\u3002\u4eca\u56de\u306e\u57fa\u790e\u3092\u571f\u53f0\u3068\u3057\u3066\u3001\u8208\u5473\u306e\u3042\u308b\u5fdc\u7528\u5206\u91ce\u3067\u78ba\u7387\u904e\u7a0b\u3092\u6d3b\u7528\u3057\u3066\u307f\u3066\u304f\u3060\u3055\u3044\u3002\u3000<\/p>\r\n<p><!-- 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[&hellip;]<\/p>\n","protected":false},"author":89,"featured_media":7137,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"content-type":"","swell_btn_cv_data":"","footnotes":"","_wp_rev_ctl_limit":""},"categories":[1246],"tags":[894,484,57],"class_list":["post-7144","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-data-infrastructure","tag-r","tag-484","tag-57"],"_links":{"self":[{"href":"https:\/\/since2020.jp\/media\/wp-json\/wp\/v2\/posts\/7144","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/since2020.jp\/media\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/since2020.jp\/media\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/since2020.jp\/media\/wp-json\/wp\/v2\/users\/89"}],"replies":[{"embeddable":true,"href":"https:\/\/since2020.jp\/media\/wp-json\/wp\/v2\/comments?post=7144"}],"version-history":[{"count":0,"href":"https:\/\/since2020.jp\/media\/wp-json\/wp\/v2\/posts\/7144\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/since2020.jp\/media\/wp-json\/wp\/v2\/media\/7137"}],"wp:attachment":[{"href":"https:\/\/since2020.jp\/media\/wp-json\/wp\/v2\/media?parent=7144"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/since2020.jp\/media\/wp-json\/wp\/v2\/categories?post=7144"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/since2020.jp\/media\/wp-json\/wp\/v2\/tags?post=7144"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}