{"id":41566,"date":"2024-07-09T05:49:04","date_gmt":"2024-07-09T05:49:04","guid":{"rendered":"https:\/\/science-hub.click\/%E3%83%9E%E3%83%AB%E3%82%B3%E3%83%95%E7%89%B9%E6%80%A7%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6%E8%A9%B3%E3%81%97%E3%81%8F%E8%A7%A3%E8%AA%AC\/"},"modified":"2024-07-09T05:49:04","modified_gmt":"2024-07-09T05:49:04","slug":"%E3%83%9E%E3%83%AB%E3%82%B3%E3%83%95%E7%89%B9%E6%80%A7%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6%E8%A9%B3%E3%81%97%E3%81%8F%E8%A7%A3%E8%AA%AC","status":"publish","type":"post","link":"https:\/\/science-hub.click\/?p=41566","title":{"rendered":"\u30de\u30eb\u30b3\u30d5\u7279\u6027\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac"},"content":{"rendered":"<div><div><h2>\u5c0e\u5165<\/h2><p>\u78ba\u7387\u306b\u304a\u3044\u3066\u3001\u78ba\u7387\u904e\u7a0b\u306f<b>\u3001<\/b>\u904e\u53bb\u306e\u72b6\u614b\u3068\u73fe\u5728\u306e\u72b6\u614b\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u306b\u3001\u5c06\u6765\u306e\u72b6\u614b\u306e\u6761\u4ef6\u4ed8\u304d\u78ba\u7387\u5206\u5e03\u304c\u5b9f\u969b\u306b\u73fe\u5728\u306e\u72b6\u614b\u306e\u307f\u306b\u4f9d\u5b58\u3057\u3001\u904e\u53bb\u306e\u72b6\u614b\u306b\u306f\u4f9d\u5b58\u3057\u306a\u3044\uff08\u300c\u8a18\u61b6\u300d\u304c\u5b58\u5728\u3057\u306a\u3044\uff09\u5834\u5408\u306b\u9650\u308a\u3001\u30de\u30eb\u30b3\u30d5\u7279\u6027\u3092\u6e80\u305f\u3057\u307e\u3059\u3002 \u3002\u3053\u306e\u6027\u8cea\u3092\u6301\u3064\u30d7\u30ed\u30bb\u30b9\u306f<b>\u30de\u30eb\u30b3\u30d5\u30d7\u30ed\u30bb\u30b9<\/b>\u3068\u547c\u3070\u308c\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306a\u30d7\u30ed\u30bb\u30b9\u3067\u306f\u3001<span><a href=\"https:\/\/science-hub.click\/?p=95909\">\u904e\u53bb<\/a><\/span>\u3068\u73fe\u5728\u3092\u77e5\u3063\u3066\u3044\u308b\u5834\u5408\u306b<span><a href=\"https:\/\/science-hub.click\/?p=45426\">\u5c06\u6765<\/a><\/span>\u306b\u3064\u3044\u3066\u884c\u3046\u3053\u3068\u304c\u3067\u304d\u308b\u6700\u826f\u306e\u4e88\u6e2c\u306f\u3001\u73fe\u5728\u3060\u3051\u3092\u77e5\u3063\u3066\u3044\u308b\u5834\u5408\u306b\u5c06\u6765\u306b\u3064\u3044\u3066\u884c\u3046\u3053\u3068\u304c\u3067\u304d\u308b\u6700\u826f\u306e\u4e88\u6e2c\u3068\u540c\u3058\u3067\u3059\u3002\u3064\u307e\u308a\u3001\u73fe\u5728\u3092\u77e5\u3063\u3066\u3044\u308c\u3070\u3001\u904e\u53bb\u306e\u77e5\u8b58\u3082\u540c\u3058\u3067\u3059\u3002\u5c06\u6765\u306e\u4e88\u6e2c\u306b\u5f79\u7acb\u3064\u8ffd\u52a0\u60c5\u5831\u3092\u63d0\u4f9b\u3057\u306a\u3044\u3053\u3068\u3002<\/p><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\u30de\u30eb\u30b3\u30d5\u7279\u6027\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/5IjUrDsHuJ4\/0.jpg\" style=\"width:100%;\"\/><\/figure><h2>\u5f31\u3044\u30de\u30eb\u30b3\u30d5\u7279\u6027 (\u96e2\u6563\u6642\u9593\u3001\u96e2\u6563\u7a7a\u9593)<\/h2><h3><span><span><a href=\"https:\/\/science-hub.click\/?p=74671\">\u610f\u5473<\/a><\/span><\/span><\/h3><p>\u3053\u308c\u306f\u30de\u30eb\u30b3\u30d5<span><a href=\"https:\/\/science-hub.click\/?p=78679\">\u9023\u9396<\/a><\/span>\u306e\u7279\u5fb4\u7684\u306a\u6027\u8cea\u3067\u3059\u3002\u57fa\u672c\u7684\u306b\u3001\u73fe\u5728\u304b\u3089\u672a\u6765\u3092\u4e88\u6e2c\u3059\u308b\u3053\u3068\u306f\u3001\u904e\u53bb\u306b\u95a2\u3059\u308b\u8ffd\u52a0\u60c5\u5831\u306b\u3088\u3063\u3066\u3088\u308a\u6b63\u78ba\u306b\u306a\u308b\u3053\u3068\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u306a\u305c\u306a\u3089\u3001\u672a\u6765\u306e\u4e88\u6e2c\u306b\u5f79\u7acb\u3064\u3059\u3079\u3066\u306e\u60c5\u5831\u306f\u73fe\u5728\u306e\u72b6\u614b\u306b\u542b\u307e\u308c\u3066\u3044\u308b\u304b\u3089\u3067\u3059\u3002\u30d7\u30ed\u30bb\u30b9\u3002\u5f31\u3044\u30de\u30eb\u30b3\u30d5\u7279\u6027\u306b\u306f\u3044\u304f\u3064\u304b\u306e\u7b49\u4fa1\u306a\u5f62\u5f0f\u304c\u3042\u308a\u3001\u305d\u308c\u3089\u306f\u3059\u3079\u3066\u6b21\u306e\u6761\u4ef6\u6cd5\u5247\u3092\u8ff0\u3079\u3066\u3044\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ X_{n+1}\\ } $$<\/div>\u904e\u53bb\u3092\u77e5\u308b\u3001\u3064\u307e\u308a\u77e5\u308b\u3053\u3068<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ \\left(X_k\\right)_{0\\le k\\le n}\\ } $$<\/div>\u306e\u95a2\u6570\u3067\u3059<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ X_n\\ } $$<\/div>\u4e00\u4eba\u3067 \uff1a<\/p><div><p> <strong>\u300c\u521d\u6b69\u7684\u306a\u300d\u5f31\u3044\u30de\u30eb\u30b3\u30d5\u7279\u6027<\/strong><span>\u2014<\/span><span><a href=\"https:\/\/science-hub.click\/?p=95765\">\u3059\u3079\u3066\u306b<\/a><\/span><div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ n\\ge 0,\\ } $$<\/div>\u4efb\u610f\u306e\u72b6\u614b\u30b7\u30fc\u30b1\u30f3\u30b9\u306b\u5bfe\u3057\u3066<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ (i_0,\\ldots,i_{n-1},i,j)\\in E^{n+2},\\ } $$<\/div><\/p><\/div><p>\u79c1\u305f\u3061\u306f\u307b\u3068\u3093\u3069\u306e\u5834\u5408\u3001<b>\u5747\u4e00\u306a<\/b>\u30de\u30eb\u30b3\u30d5\u9023\u9396\u3092\u4eee\u5b9a\u3057\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u9077\u79fb\u30e1\u30ab\u30cb\u30ba\u30e0\u306f<span><a href=\"https:\/\/science-hub.click\/?p=82055\">\u6642\u9593<\/a><\/span>\u306e\u7d4c\u904e\u3068\u3068\u3082\u306b\u5909\u5316\u3057\u306a\u3044\u3068\u4eee\u5b9a\u3057\u307e\u3059\u3002<b>\u5f31\u3044\u30de\u30eb\u30b3\u30d5\u7279\u6027\u306f<\/b>\u6b21\u306e\u5f62\u5f0f\u306b\u306a\u308a\u307e\u3059\u3002 <\/p><dl><dd><div class=\"math-formual notranslate\">$$ {\\forall n\\ge 0, \\forall (i_0,\\ldots,i_{n-1},i,j) \\in E^{n+2},} $$<\/div><dl><dd><div class=\"math-formual notranslate\">$$ {\\mathbb{P}\\Big(X_{n+1}=j \\mid\\, X_0=i_0, X_1=i_1,\\ldots, X_{n-1}=i_{n-1},X_n=i\\Big) = \\mathbb{P}\\left(X_{1}=j\\mid X_0=i\\right). } $$<\/div><\/dd><\/dl><\/dd><\/dl><p>\u5f31\u3044\u30de\u30eb\u30b3\u30d5\u7279\u6027\u306e\u3053\u306e\u5f62\u5f0f\u306f\u3001\u524d\u306e\u5f62\u5f0f\u3088\u308a\u3082\u5f37\u529b\u3067\u3042\u308a\u3001\u7279\u306b\u6b21\u306e\u3088\u3046\u306a\u7d50\u679c\u306b\u3064\u306a\u304c\u308a\u307e\u3059\u3002 <\/p><dl><dd><div class=\"math-formual notranslate\">$$ {\\forall n\\ge 0, \\forall (i,j)\\in E^{2},\\qquad\\mathbb{P}\\left(X_{n+1}=j\\mid X_n=i\\right) = \\mathbb{P}\\left(X_{1}=j\\mid X_0=i\\right).} $$<\/div><\/dd><\/dl><p>\u3053\u306e\u8a18\u4e8b\u306e\u6b8b\u308a\u306e\u90e8\u5206\u3067\u306f\u3001\u540c\u7a2e\u30de\u30eb\u30b3\u30d5\u9023\u9396\u306e\u307f\u3092\u8003\u616e\u3057\u307e\u3059\u3002<i>\u4e0d\u5747\u4e00<\/i>\u30de\u30eb\u30b3\u30d5\u9023\u9396\u306e<span><a href=\"https:\/\/science-hub.click\/?p=16388\">\u7d44\u307f\u5408\u308f\u305b\u6700\u9069\u5316<\/a><\/span>\u3078\u306e\u8208\u5473\u6df1\u3044\u5fdc\u7528\u306b\u3064\u3044\u3066\u306f\u3001\u300c\u30b7\u30df\u30e5\u30ec\u30fc\u30c6\u30c3\u30c9 \u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u300d\u306e\u8a18\u4e8b\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p><p>\u540c\u7a2e\u30de\u30eb\u30b3\u30d5\u9023\u9396\u306e\u5f31\u3044\u30de\u30eb\u30b3\u30d5\u7279\u6027\u306b\u306f\u5225\u306e\u5f62\u5f0f\u304c\u3042\u308a\u3001\u524d\u306e\u5f62\u5f0f\u3088\u308a\u3082\u306f\u308b\u304b\u306b\u4e00\u822c\u7684\u3067\u3059\u304c\u3001\u305d\u308c\u3067\u3082\u524d\u306e\u5f62\u5f0f\u3068\u540c\u7b49\u3067\u3059\u3002<\/p><div><p> <strong>\u300c\u4e00\u822c\u300d\u306e\u5f31\u3044\u30de\u30eb\u30b3\u30d5\u7279\u6027<\/strong><span>\u2014<\/span>\u4efb\u610f\u306e\u9078\u629e\u306b\u5bfe\u3057\u3066<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ n\\ge 0,\\quad B\\in \\mathcal P(E)^{\\otimes{\\mathbb N}},\\quad A\\in \\mathcal P(E^{n+1}),\\quad i\\in E,} $$<\/div><\/p><dl><dd><div class=\"math-formual notranslate\">$$ {{\\mathbb P}((X_{n}, X_{n+1}, \\dots ) \\in B\\,|\\,(X_0,\\dots,X_{n}) \\in A,  X_n=i) \\;=\\;{\\mathbb P}((X_{0}, X_{1}, \\dots )\\in B\\,|\\, X_0=i).} $$<\/div><\/dd><\/dl><\/div><p>\u904e\u53bb\u306e\u51fa\u6765\u4e8b\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ \\{(X_0,\\dots,X_{n}) \\in A\\}\\ } $$<\/div>\u305d\u3057\u3066\u672a\u6765<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ \\{(X_{n}, X_{n+1}, \\dots ) \\in B\\}\\ } $$<\/div>\u3053\u3053\u3067\u306f\u53ef\u80fd\u306a\u9650\u308a\u6700\u3082\u4e00\u822c\u7684\u306a\u5f62\u5f0f\u3092\u3068\u308a\u307e\u3059\u304c\u3001\u73fe\u5728\u306e\u30a4\u30d9\u30f3\u30c8\u306f<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ \\{X_n=i\\}\\ } $$<\/div>\u5076\u7136\u3067\u306f\u306a\u304f\u3001\u7279\u5b9a\u306e\u5f62\u3067\u6b8b\u308a\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ \\{X_n=i\\}\\ } $$<\/div>\u306b\u3088\u308b<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ \\{X_n\\in C\\}\\ } $$<\/div>\u4e0a\u8a18\u306e\u30b9\u30c6\u30fc\u30c8\u30e1\u30f3\u30c8\u3067\u306f\u3001\u904e\u53bb\u306b\u95a2\u3059\u308b\u60c5\u5831\u304c\u73fe\u5728\u3092\u4e88\u6e2c\u3059\u308b\u306e\u306b\u5f79\u7acb\u3064\u305f\u3081\u3001\u3053\u306e\u30b9\u30c6\u30fc\u30c8\u30e1\u30f3\u30c8\u306f\u4e00\u822c\u7684\u306b\u507d\u306b\u306a\u308a\u307e\u3059 (\u305f\u3060\u3057\u3001 <div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ X_n\\ } $$<\/div>\u3088\u308a\u6b63\u78ba\u306b\u306f\u3001\u90e8\u54c1\u306e\u5185\u90e8\u3067\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u304b<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ C\\ } $$<\/div> ?)\u3001\u305d\u3053\u304b\u3089\u672a\u6765\u3092\u4e88\u6e2c\u3057\u307e\u3059\u3002<\/p><div> <strong><span><a href=\"https:\/\/science-hub.click\/?p=85529\">\u30e9\u30f3\u30c0\u30e0\u30a6\u30a9\u30fc\u30af<\/a><\/span>\u306e\u53cd\u4f8b<\/strong>$$ {\\scriptstyle\\ \\mathbb{Z}\\ } $$<\/div> :<div><p>\u3082\u3057<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ E=\\mathbb{Z}\\ } $$<\/div>\u305d\u3057\u3066<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ p_{i,i+1}=1-p_{i,i-1}=p,\\ } $$<\/div><i>\u30e9\u30f3\u30c0\u30e0\u30a6\u30a9\u30fc\u30af<\/i>\u306b\u3064\u3044\u3066\u8a71\u3057\u307e\u3059<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ \\mathbb{Z}.\\ } $$<\/div>\u6b21\u306e\u3088\u3046\u306b\u4eee\u5b9a\u3057\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ p\\in]0,1[.\\ } $$<\/div>\u3057\u305f\u304c\u3063\u3066\u3001\u305f\u3068\u3048\u3070\u3001 <\/p><dl><dd><div class=\"math-formual notranslate\">$$ {\\mathbb{P}_{\\mu}(X_{n+1}=1\\ |\\ X_n\\in\\{0,1\\}\\text{ et }X_{n-1}=0)=0,\\ } $$<\/div><\/dd><\/dl><p>\u79c1\u305f\u3061\u306f\u7c21\u5358\u306b\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u304c\u3001 <div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ \\mu\\ } $$<\/div>\u305d\u3057\u3066<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ n\\ } $$<\/div>\u306e\u3088\u3046\u306a<\/p><dl><div class=\"math-formual notranslate\">$$ {\\mathbb{P}_{\\mu}(X_{n+1}=1\\ |\\ X_n\\in\\{0,1\\})&gt;0.\\ } $$<\/div><\/dl><p>\u3057\u305f\u304c\u3063\u3066\u3001<i>\u4e0d\u6b63\u78ba\u306a<\/i>\u77e5\u8b58\u306b\u3088\u308a\uff08 <div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ \\{X_n\\in \\{0,1\\}\\}\\  } $$<\/div> ) \u73fe\u5728\u3001\u904e\u53bb\u306b\u95a2\u3059\u308b\u7279\u5b9a\u306e\u60c5\u5831\u306b\u3088\u308a\u3001\u4e88\u5f8c\u3092\u6539\u5584\u3059\u308b\u3053\u3068\u304c\u53ef\u80fd\u306b\u306a\u308a\u307e\u3059\u3002X <i><sub>n-1<\/sub> = 0 \u304c\u308f\u304b\u3063<\/i>\u3066\u3044\u308b\u305f\u3081\u3001 <i>X <sub>n \u306f<\/sub><\/i>\u30bc\u30ed\u3067\u306f\u306a\u3044\u3068\u63a8\u6e2c\u3055\u308c\u3001\u3057\u305f\u304c\u3063\u3066<i>X <sub>n \u306f<\/sub><\/i>1 \u306b\u7b49\u3057\u3044\u3068\u7d50\u8ad6\u4ed8\u3051\u3089\u308c\u307e\u3059<i>\u3002 <sub>n+1 \u3092<\/sub><\/i>1 \u306b\u7b49\u3057\u304f\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002\u4e00\u65b9\u3001 <i>X <sub>n-1<\/sub> = 0<\/i>\u3068\u3044\u3046\u60c5\u5831\u304c\u306a\u3051\u308c\u3070\u3001 <i>X <sub>n+1<\/sub><\/i>\u304c 1 \u306b\u7b49\u3057\u3044\u3053\u3068\u3092\u9664\u5916\u3067\u304d\u307e\u305b\u3093\u3002<\/p><p>\u305f\u3060\u3057\u3001\u30e9\u30f3\u30c0\u30e0\u30a6\u30a9\u30fc\u30af\u306f<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\  \\mathbb{Z}\\ } $$<\/div>\u306f\u30de\u30eb\u30b3\u30d5\u9023\u9396\u3067\u3042\u308a\u3001\u5b9f\u969b\u306b\u30de\u30eb\u30b3\u30d5\u7279\u6027\u3092\u6301\u3063\u3066\u3044\u307e\u3059\u3002\u3053\u3053\u306b\u77db\u76fe\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u30de\u30eb\u30b3\u30d5\u306e\u6027\u8cea\u306f\u3001\u73fe\u5728\u306e<i><b>\u6b63\u78ba\u306a<\/b><\/i>\u77e5\u8b58 ( <i>X <sub>n<\/sub> = i<\/i> ) \u304c\u3042\u308c\u3070\u3001\u904e\u53bb\u306b\u95a2\u3059\u308b\u60c5\u5831\u304c\u306a\u304f\u3066\u3082\u4e88\u5f8c\u3092\u6539\u5584\u3067\u304d\u308b\u3068<span><a href=\"https:\/\/science-hub.click\/?p=16042\">\u8ff0\u3079<\/a><\/span>\u3066\u3044\u307e\u3059\u3002<\/p><\/div><\/div><p><b>\u6642\u9593\u505c\u6b62<\/b>\u306e\u6982\u5ff5\u306b\u95a2\u9023\u3059\u308b \u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u5f37\u529b\u306a\u30de\u30eb\u30b3\u30d5\u7279\u6027\u306f\u3001\u91cd\u8981\u306a\u7d50\u679c (\u3055\u307e\u3056\u307e\u306a\u53cd\u5fa9\u57fa\u6e96\u3001\u30de\u30eb\u30b3\u30d5\u9023\u9396\u306e\u5f37\u529b\u306a\u5927\u6570\u306e\u6cd5\u5247) \u3092<span><a href=\"https:\/\/science-hub.click\/?p=52981\">\u5b9f\u8a3c\u3059\u308b<\/a><\/span>\u305f\u3081\u306b\u91cd\u8981\u3067\u3059\u3002<\/p><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\u30de\u30eb\u30b3\u30d5\u7279\u6027\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/1eVd83SldBY\/0.jpg\" style=\"width:100%;\"\/><\/figure><h3><span>\u6761\u4ef6\u4ed8\u304d\u72ec\u7acb\u6027<\/span><\/h3><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\u30de\u30eb\u30b3\u30d5\u7279\u6027\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/gVSGdpcl8Pw\/0.jpg\" style=\"width:100%;\"\/><\/figure><p>\u300c\u4e00\u822c\u7684\u306a\u300d\u5f31\u3044\u30de\u30eb\u30b3\u30d5\u7279\u6027\u306f\u3001\u6b21\u306e\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002<\/p><div><p><strong>\u6761\u4ef6\u4ed8\u304d\u72ec\u7acb\u6027<\/strong><span>\u2014<\/span>\u4efb\u610f\u306e\u9078\u629e\u306b\u5bfe\u3057\u3066<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ n\\ge 0,\\quad B\\in \\mathcal P(E)^{\\otimes{\\mathbb N}},\\quad A\\in \\mathcal P(E^{n+1}),\\quad i\\in E,} $$<\/div><\/p><dl><dd><div class=\"math-formual notranslate\">$$ {{\\mathbb P}((X_{n}, X_{n+1}, \\dots ) \\in B\\text{ et } (X_0,\\dots,X_{n}) \\in A\\ |\\ X_n=i)} $$<\/div><dl><dd><div class=\"math-formual notranslate\">$$ {=\\;{\\mathbb P}((X_{n}, X_{n+1}, \\dots ) \\in B\\ |\\ X_n=i)\\times{\\mathbb P}((X_0,\\dots,X_{n}) \\in A\\ |\\  X_n=i). } $$<\/div><\/dd><\/dl><\/dd><\/dl><\/div><p>\u3053\u306e\u7b49\u5f0f\u306f<i>\u3001\u73fe\u5728\u3092\u77e5\u3063\u3066\u3044\u308b\uff08\u305d\u308c\u3092\u77e5\u3063\u3066\u3044\u308b\uff09\u3001\u904e\u53bb\u3068\u672a\u6765\u306e\u9593\u306e\u6761\u4ef6\u4ed8\u304d\u72ec\u7acb\u6027<\/i>\u3092\u8868\u3057\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ X_n=i\\ } $$<\/div> \uff09\u3002\u305f\u3060\u3057\u3001\u4e0a\u8a18\u306e\u300c\u4e00\u822c\u7684\u306a\u300d\u5f31\u3044\u30de\u30eb\u30b3\u30d5\u7279\u6027\u3068\u6bd4\u8f03\u3059\u308b\u3068\u3001\u5747\u4e00\u6027\u7279\u6027\u304c\u5931\u308f\u308c\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u300c\u4e00\u822c\u7684\u306a\u300d\u5f31\u3044\u30de\u30eb\u30b3\u30d5\u7279\u6027\u306f\u3001\u5b9f\u969b\u306b\u306f\u3088\u308a\u5f37\u3044\u7279\u6027\u3068\u540c\u7b49\u3067\u3059\u3002<\/p><div><p><strong>\u6761\u4ef6\u4ed8\u304d\u306e\u72ec\u7acb\u6027\u3068\u5747\u4e00\u6027<\/strong><span>\u2014<\/span>\u3042\u3089\u3086\u308b\u9078\u629e\u306b\u5bfe\u3057\u3066<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ n\\ge 0,\\quad B\\in \\mathcal P(E)^{\\otimes{\\mathbb N}},\\quad A\\in \\mathcal P(E^{n+1}),\\quad i\\in E,} $$<\/div><\/p><dl><dd><div class=\"math-formual notranslate\">$$ {{\\mathbb P}((X_{n}, X_{n+1}, \\dots ) \\in B\\text{ et } (X_0,\\dots,X_{n}) \\in A\\ |\\ X_n=i)} $$<\/div><dl><dd><div class=\"math-formual notranslate\">$$ { =\\; {\\mathbb P}((X_{0}, X_{1}, \\dots )\\in B\\ |\\ X_0=i)\\times{\\mathbb P}((X_0,\\dots,X_{n}) \\in A\\ |\\  X_n=i). } $$<\/div><\/dd><\/dl><\/dd><\/dl><\/div><h3><span>\u57fa\u6e96<\/span><\/h3><div><p><strong>\u57fa\u672c\u7684\u306a\u57fa\u6e96<\/strong><span>\u2014<\/span>\u30b7\u30fc\u30b1\u30f3\u30b9\u306e\u3044\u305a\u308c\u304b<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ Y=(Y_{n})_{n\\ge 0}\\ } $$<\/div>\u72ec\u7acb\u3057\u305f\u78ba\u7387\u5909\u6570\u3068\u540c\u3058\u6cd5\u5247\u3001\u7a7a\u9593\u5185\u306e\u5024\u3092\u6301\u3064<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ F\\ } $$<\/div> \u3001\u304a\u3088\u3073\u3044\u305a\u308c\u304b<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ f\\ } $$<\/div>\u6e2c\u5b9a\u53ef\u80fd\u306a\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ E\\times F\\ } $$<\/div>\u3067<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ E.\\ } $$<\/div>\u6b21\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u304c\u3042\u308b\u3068\u3057\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ X=(X_{n})_{n\\ge 0}\\ } $$<\/div>\u306f\u6f38\u5316\u95a2\u4fc2\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002 <\/p><dl><dd><div class=\"math-formual notranslate\">$$ {\\forall n\\ge 0,\\qquad X_{n+1}=f\\left(X_n,Y_{n}\\right),} $$<\/div><\/dd><\/dl><p>\u305d\u3057\u3066\u6b21\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u304c\u3042\u308b\u3068\u4eee\u5b9a\u3057\u307e\u3059<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ Y\\ } $$<\/div>\u304b\u3089\u72ec\u7acb\u3057\u3066\u3044\u307e\u3059<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ X_0.\\ } $$<\/div>\u305d\u308c\u3067<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ X\\ } $$<\/div>\u306f\u540c\u7a2e\u30de\u30eb\u30b3\u30d5\u9023\u9396\u3067\u3059\u3002<\/p><\/div><div><strong>\u30b9\u30c6\u30c3\u30ab\u30fc\u30b3\u30ec\u30af\u30bf\u30fc\uff08\u30b3\u30ec\u30af\u30bf\u30fc\u30af\u30fc\u30dd\u30f3\uff09\uff1a<\/strong><div><p>\u30d7\u30c6\u30a3\u30fb\u30d4\u30a8\u30fc\u30eb\u306f\u3001\u30b5\u30c3\u30ab\u30fc\u4ee3\u8868\u30c1\u30fc\u30e0\u306e 11 \u4eba\u306e\u9078\u624b\u306e\u30dd\u30fc\u30c8\u30ec\u30fc\u30c8\u3092\u53ce\u96c6\u3057\u3066\u304a\u308a\u3001\u30bb\u30e2\u30ef\u306e\u30c1\u30e7\u30b3\u30ec\u30fc\u30c8 \u30d0\u30fc\u306e\u30d1\u30c3\u30b1\u30fc\u30b8\u5185\u306e\u30b9\u30c6\u30c3\u30ab\u30fc\u306b\u305d\u308c\u3089\u306e\u30dd\u30fc\u30c8\u30ec\u30fc\u30c8\u304c\u8cbc\u3089\u308c\u3066\u3044\u308b\u306e\u3092\u898b\u3064\u3051\u307e\u3059\u3002\u5f7c\u304c\u30bf\u30d6\u30ec\u30c3\u30c8\u3092\u8cfc\u5165\u3059\u308b\u305f\u3073\u306b\u300111 \u5206\u306e 1 \u306e\u78ba\u7387\u3067\u9078\u624b\u756a\u53f7 2 \u306e\u8096\u50cf\u753b\u306b\u906d\u9047\u3057\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ k\\ } $$<\/div> (\u3059\u3079\u3066\u306b\u3064\u3044\u3066<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ k\\ } $$<\/div> \uff09\u3002\u6ce8\u610f\u3057\u307e\u3059<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ X_{n}\\in\\mathcal{P}([\\![ 1,11]\\!])\\ } $$<\/div>\u30d7\u30c6\u30a3\u30fb\u30d4\u30a8\u30fc\u30eb\u306e\u30b3\u30ec\u30af\u30b7\u30e7\u30f3\u306e\u68b1\u5305\u3092\u958b\u3051\u305f\u5f8c\u306e\u72b6\u614b<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ n\\ } $$<\/div> &#8211; \u756a\u76ee\u306e\u30c1\u30e7\u30b3\u30ec\u30fc\u30c8\u30d0\u30fc\u3002 <div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ X=(X_{n})_{n\\ge 0}\\ } $$<\/div>\u306f\u6b21\u304b\u3089\u59cb\u307e\u308b\u30de\u30eb\u30b3\u30d5\u9023\u9396\u3067\u3059<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ X_{0}=\\emptyset\\ } $$<\/div> \u3001\u305d\u308c\u306f\u4ee5\u524d\u306e\u9078\u629e\u306e\u67a0\u7d44\u307f\u306b\u9069\u5408\u3059\u308b\u305f\u3081\u3067\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ F=[\\![1,11]\\!],\\ E=\\mathcal{P}(F),\\ f(x,y)=x\\cup\\{y\\},\\ } $$<\/div>\u4ee5\u6765<\/p><dl><dd><div class=\"math-formual notranslate\">$$ { X_{n+1}=X_n\\cup\\{Y_n\\},} $$<\/div><\/dd><\/dl><p>\u3053\u3053\u3067\u3001\u78ba\u7387\u5909\u6570\u306f<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ Y_{n}\\ } $$<\/div>\u306f\u72ec\u7acb\u3057\u305f\u4e00\u69d8\u306a\u78ba\u7387\u5909\u6570\u3067\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ [\\![1,11]\\!]\\ } $$<\/div> : \u3053\u308c\u3089\u306f\u30c1\u30e7\u30b3\u30ec\u30fc\u30c8\u30d0\u30fc\u304b\u3089\u53d6\u3089\u308c\u305f\u30b7\u30fc\u30eb\u306e\u9023\u7d9a\u756a\u53f7\u3067\u3059\u3002\u30b3\u30ec\u30af\u30b7\u30e7\u30f3\u3092\u5b8c\u6210\u3055\u305b\u308b\u306e\u306b\u5fc5\u8981\u306a\u5e73\u5747\u6642\u9593 (\u3053\u3053\u3067\u306f\u3001\u30d7\u30c6\u30a3\u30fb\u30d4\u30a8\u30fc\u30eb\u304c\u30b3\u30ec\u30af\u30b7\u30e7\u30f3\u3092\u5b8c\u6210\u3055\u305b\u308b\u305f\u3081\u306b\u5e73\u5747\u3057\u3066\u8cfc\u5165\u3057\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u9320\u5264\u306e\u6570) \u306f\u3001 <div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ N\\ } $$<\/div>\u5408\u8a08\u30b5\u30e0\u30cd\u30a4\u30eb\u3001 <div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ N\\,H_N,\\ } $$<\/div>\u307e\u305f\u306f<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ H_N\\ } $$<\/div>\u3067\u3059<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ N\\ } $$<\/div> -\u6b21\u9ad8\u8abf\u6ce2\u756a\u53f7\u3002\u4f8b\u3048\u3070\u3001 <div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ 11\\,H_{11}=33,2\\dots\\quad } $$<\/div>\u30c1\u30e7\u30b3\u30ec\u30fc\u30c8\u30d0\u30fc\u3002<\/p><\/div><\/div><div><strong>\u5099\u8003\uff1a<\/strong><div><ul><li>\u30de\u30eb\u30b3\u30d5\u7279\u6027\u306f\u3001\u6b21\u306e\u72ec\u7acb\u6027\u304b\u3089\u751f\u3058\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ Y_i\\\u00a0;\\ } $$<\/div>\u6b21\u306e\u5834\u5408\u306f true \u306e\u307e\u307e\u3067\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ Y_i\\ } $$<\/div>\u7570\u306a\u308b\u6cd5\u5247\u304c\u3042\u308a\u3001\u300c\u518d\u5e30\u95a2\u4fc2\u300d\u304c\u6210\u7acb\u3059\u308b\u3068\u304d<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ X_{n+1}=f_n\\left(X_n,Y_{n}\\right)\\ } $$<\/div>\u306b\u4f9d\u5b58\u3057\u307e\u3059<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ n.\\ } $$<\/div>\u72ec\u7acb\u6027\u306b\u52a0\u3048\u3066\u884c\u308f\u308c\u308b\u4eee\u5b9a\u306f\u3001\u30de\u30eb\u30b3\u30d5\u9023\u9396\u306e\u5747\u4e00\u6027\u3092\u4fdd\u8a3c\u3059\u308b\u305f\u3081\u3060\u3051\u306b\u5b58\u5728\u3057\u307e\u3059\u3002<\/li><li>\u3053\u306e\u57fa\u6e96\u306f\u3001\u6b21\u306e\u5f62\u5f0f\u306e\u53cd\u5fa9\u306b\u3088\u3063\u3066\u5747\u8cea\u306a\u30de\u30eb\u30b3\u30d5\u9023\u9396\u3092\u6b63\u78ba\u306b\u30b7\u30df\u30e5\u30ec\u30fc\u30c8\u3067\u304d\u308b\u3068\u3044\u3046\u70b9\u3067\u57fa\u672c\u7684\u3067\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ X_{n+1}=f\\left(X_n,Y_{n}\\right),\\ } $$<\/div>\u6a5f\u80fd\u306e\u305f\u3081\u306b<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ f\\ } $$<\/div>\u3088\u304f\u9078\u3070\u308c\u307e\u3057\u305f\u3002\u3088\u308a\u6b63\u78ba\u306b\u8a00\u3048\u3070\u3001 <div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ X=(X_{n})_{n\\ge 0}\\ } $$<\/div>\u306f\u540c\u6b21\u30de\u30eb\u30b3\u30d5\u9023\u9396\u3067\u3042\u308a\u30015 \u3064\u306e\u8981\u7d20\u304c\u5b58\u5728\u3057\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ (\\Omega,\\mathcal{A},\\mathbb{P},X^{\\prime}_0,Y),\\ } $$<\/div>\u307e\u305f\u306f<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ (\\Omega,\\mathcal{A},\\mathbb{P})\\ } $$<\/div>\u306f\u78ba\u7387\u7a7a\u9593\u3092\u8868\u3057\u3001 <div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ X^{\\prime}_0\\ } $$<\/div>\u306e\u5024\u3092\u6301\u3064\u78ba\u7387\u5909\u6570\u3067\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ E\\ } $$<\/div>\u305d\u3057\u3066\u3069\u3053\u3067<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ Y=(Y_{n})_{n\\ge 0}\\ } $$<\/div>\u306e\u5024\u3092\u6301\u3064\u4e00\u9023\u306e iid \u78ba\u7387\u5909\u6570\u3067\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ F,\\ \\ } $$<\/div><div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ X^{\\prime}_0\\ } $$<\/div>\u305d\u3057\u3066<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ Y\\ } $$<\/div>\u306b\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u308b<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ (\\Omega,\\mathcal{A},\\mathbb{P})\\ } $$<\/div>\u72ec\u7acb\u3057\u3066\u3044\u3066\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u304c\u3042\u308a\u307e\u3059<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ f\\ \\ } $$<\/div>\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u308b<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ E\\times F\\ } $$<\/div>\u3067<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ E,\\ } $$<\/div>\u6b21\u306e\u3088\u3046\u306a<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ X^{\\prime}=(X^{\\prime}_{n})_{n\\ge 0}\\ } $$<\/div>\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u308b<\/li><\/ul><dl><dd><div class=\"math-formual notranslate\">$$ { X^{\\prime}_{n+1}=f(X^{\\prime}_n,Y_n)} $$<\/div><\/dd><dd>\u4ed6\u3068\u540c\u3058\u6cd5\u5247\u304c\u3042\u308b<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ X=(X_{n})_{n\\ge 0}.\\ } $$<\/div><\/dd><\/dl><ul><li>\u9078\u629e\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ F=[0,1],\\ } $$<\/div>\u305d\u3057\u3066\u5909\u6570\u3092\u9078\u629e\u3057\u307e\u3059<div class=\"math-formual notranslate\">$$ {\\scriptstyle\\ Y_{j}\\ } $$<\/div>\u3053\u308c\u306f\u3001\u30e2\u30f3\u30c6\u30ab\u30eb\u30ed\u6cd5\u306b\u3088\u308b\u30de\u30eb\u30b3\u30d5\u9023\u9396\u306e\u7814\u7a76\u3001\u3064\u307e\u308a\u30de\u30eb\u30b3\u30d5\u9023\u9396\u306e\u300c\u5178\u578b\u7684\u306a\u300d\u8ecc\u9053\u306e\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u306b\u3088\u308b\u30de\u30eb\u30b3\u30d5\u9023\u9396\u306e\u7814\u7a76\u306b\u4fbf\u5229\u3067\u3059\u3002<\/li><\/ul><\/div><\/div><\/div>\n<h2 class=\"ref_link\">\u53c2\u8003\u8cc7\u6599<\/h2>\n<ol><li><a class=\"notranslate\" href=\"https:\/\/af.wikipedia.org\/wiki\/Markov-eienskap\">Markov-eienskap \u2013 afrikaans<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/ar.wikipedia.org\/wiki\/%D8%AE%D8%A7%D8%B5%D9%8A%D8%A9_%D9%85%D8%A7%D8%B1%D9%83%D9%88%D9%81\">\u062e\u0627\u0635\u064a\u0629 \u0645\u0627\u0631\u0643\u0648\u0641 \u2013 arabe<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/bg.wikipedia.org\/wiki\/%D0%9C%D0%B0%D1%80%D0%BA%D0%BE%D0%B2%D1%81%D0%BA%D0%BE_%D1%81%D0%B2%D0%BE%D0%B9%D1%81%D1%82%D0%B2%D0%BE\">\u041c\u0430\u0440\u043a\u043e\u0432\u0441\u043a\u043e \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u043e \u2013 bulgare<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/ca.wikipedia.org\/wiki\/Propietat_de_M%C3%A0rkov\">Propietat de M\u00e0rkov \u2013 catalan<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/de.wikipedia.org\/wiki\/Markow-Eigenschaft\">Markow-Eigenschaft \u2013 allemand<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/en.wikipedia.org\/wiki\/Markov_property\">Markov property \u2013 anglais<\/a><\/li><\/ol>\n<div class=\"feature-video\">\n <h2>\n  \u30de\u30eb\u30b3\u30d5\u7279\u6027\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\u30fb\u95a2\u9023\u52d5\u753b\n <\/h2>\n <div class=\"video-item\">\n  \n  <figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\">\n   <div class=\"wp-block-embed__wrapper\">\n    <iframe loading=\"lazy\" title=\"\u30de\u30eb\u30b3\u30d5\u904e\u7a0b[G\u691c\u5b9a\u30fb\u4e2d\u7d1a]\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/1eVd83SldBY?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n   <\/div>\n  <\/figure>\n  \n <\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5c0e\u5165 \u78ba\u7387\u306b\u304a\u3044\u3066\u3001\u78ba\u7387\u904e\u7a0b\u306f\u3001\u904e\u53bb\u306e\u72b6\u614b\u3068\u73fe\u5728\u306e\u72b6\u614b\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u306b\u3001\u5c06\u6765\u306e\u72b6\u614b\u306e\u6761\u4ef6\u4ed8\u304d\u78ba\u7387\u5206\u5e03\u304c\u5b9f\u969b\u306b\u73fe\u5728\u306e\u72b6\u614b\u306e\u307f\u306b\u4f9d\u5b58\u3057\u3001\u904e\u53bb\u306e\u72b6\u614b\u306b\u306f\u4f9d\u5b58\u3057\u306a\u3044\uff08\u300c\u8a18\u61b6\u300d\u304c\u5b58\u5728\u3057\u306a\u3044\uff09\u5834\u5408\u306b\u9650\u308a\u3001\u30de\u30eb\u30b3\u30d5\u7279\u6027\u3092\u6e80\u305f\u3057\u307e\u3059\u3002 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":41567,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"https:\/\/img.youtube.com\/vi\/-1lnJey8dJM\/0.jpg","fifu_image_alt":"\u30de\u30eb\u30b3\u30d5\u7279\u6027\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac","footnotes":""},"categories":[5],"tags":[11,13,14,10,41400,41399,12,8,16,15,9,18246],"class_list":["post-41566","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-dictionary","tag-techniques","tag-technologie","tag-news","tag-actualite","tag-markov","tag-propriete-de-markov","tag-dossier","tag-definition","tag-sciences","tag-article","tag-explications","tag-propriete"],"_links":{"self":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/posts\/41566"}],"collection":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=41566"}],"version-history":[{"count":0,"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/posts\/41566\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/media\/41567"}],"wp:attachment":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=41566"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=41566"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=41566"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}