{"id":151,"date":"2006-07-21T00:53:02","date_gmt":"2006-07-21T00:53:02","guid":{"rendered":"https:\/\/remichapeaublanc.com\/wp\/2006\/07\/21\/systeme-markovien-dordre-2\/"},"modified":"2006-07-21T00:53:02","modified_gmt":"2006-07-21T00:53:02","slug":"systeme-markovien-dordre-2","status":"publish","type":"post","link":"https:\/\/remichapeaublanc.com\/en\/systeme-markovien-dordre-2\/","title":{"rendered":"Syst\u00e8me Markovien d&#8217;ordre 2"},"content":{"rendered":"<p>En probabilit\u00e9 un processus stochastique v\u00e9rifie la propri\u00e9t\u00e9 markovienne si et seulement si la distribution conditionnelle de probabilit\u00e9 des \u00e9tats futurs, \u00e9tant donn\u00e9 l&#8217;instant pr\u00e9sent, ne d\u00e9pend que de ce m\u00eame \u00e9tat pr\u00e9sent et pas des \u00e9tats pass\u00e9s. Un processus qui poss\u00e8de cette propri\u00e9t\u00e9 est appel\u00e9 processus de Markov.<\/p>\n<p>Math\u00e9matiquement, si X(t), t &gt; 0, est un processus stochastique, la propri\u00e9t\u00e9 de Markov est d\u00e9finie ainsi&nbsp;:<\/p>\n<p><img decoding=\"async\" src=\"\/wp-content\/uploads\/images\/equation1.png\" alt=\"\" title=\"\"><\/p>\n<p>G\u00e9n\u00e9ralement, on utilise une hypoth\u00e8se d&#8217;homog\u00e9n\u00e9\u00eft\u00e9 dans le temps, c&#8217;est-\u00e0-dire<\/p>\n<p><img decoding=\"async\" src=\"\/wp-content\/uploads\/images\/equation2.png\" alt=\"\" title=\"\"><\/p>\n<p>Dans certains cas, un processus \u00e0 premi\u00e8re vue non-markovien peut tout de m\u00eame avoir des repr\u00e9sentations markoviennes en modifiant le concept d&#8217;\u00e9tat actuel et futur. Soit X un intervalle de temps et un processus Y, tel que chaque \u00e9tat de Y repr\u00e9sente un intervalle de temps de X&nbsp;:<\/p>\n<p><img decoding=\"async\" src=\"\/wp-content\/uploads\/images\/equation3.png\" alt=\"\" title=\"\"><\/p>\n<p>Si Y est markovien, alors c&#8217;est une repr\u00e9sentation markovienne de X et X est alors appel\u00e9 processus de Markov du second ordre. Les processus d&#8217;ordre sup\u00e9rieurs sont d\u00e9finis de la m\u00eame mani\u00e8re.<\/p>\n<p><img decoding=\"async\" src=\"\/wp-content\/uploads\/images\/juillet_2006\/geometrie.jpg\" alt=\"Syst\u00e8me Markovien d&#039;ordre 2\" title=\"\"><\/p>","protected":false},"excerpt":{"rendered":"<p>En probabilit\u00e9 un processus stochastique v\u00e9rifie la propri\u00e9t\u00e9 markovienne si et seulement si la distribution conditionnelle de probabilit\u00e9 des \u00e9tats futurs, \u00e9tant donn\u00e9 l&#8217;instant pr\u00e9sent, ne d\u00e9pend que de ce m\u00eame \u00e9tat pr\u00e9sent et pas des \u00e9tats pass\u00e9s. Un processus qui poss\u00e8de cette propri\u00e9t\u00e9 est appel\u00e9 processus de Markov.<\/p>","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"footnotes":""},"categories":[831],"tags":[],"class_list":["post-151","post","type-post","status-publish","format-standard","hentry","category-ancien-blog"],"_links":{"self":[{"href":"https:\/\/remichapeaublanc.com\/en\/wp-json\/wp\/v2\/posts\/151","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/remichapeaublanc.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/remichapeaublanc.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/remichapeaublanc.com\/en\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/remichapeaublanc.com\/en\/wp-json\/wp\/v2\/comments?post=151"}],"version-history":[{"count":0,"href":"https:\/\/remichapeaublanc.com\/en\/wp-json\/wp\/v2\/posts\/151\/revisions"}],"wp:attachment":[{"href":"https:\/\/remichapeaublanc.com\/en\/wp-json\/wp\/v2\/media?parent=151"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/remichapeaublanc.com\/en\/wp-json\/wp\/v2\/categories?post=151"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/remichapeaublanc.com\/en\/wp-json\/wp\/v2\/tags?post=151"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}