{"id":45,"date":"2013-11-28T20:12:28","date_gmt":"2013-11-28T19:12:28","guid":{"rendered":"http:\/\/www.latp.univ-mrs.fr\/~mathieu.dandonneau\/m2psav.new\/?page_id=45"},"modified":"2021-11-22T16:02:57","modified_gmt":"2021-11-22T15:02:57","slug":"martingales-mouvement-brownien-et-calcul-stochastique","status":"publish","type":"page","link":"https:\/\/m2psav.master.edu-math.org\/?page_id=45","title":{"rendered":"Martingales, Mouvement Brownien et calcul stochastique"},"content":{"rendered":"<p>MPSAV2-Martingales, mouvement brownien et calcul stochastique<br \/>\nModeste N\u2019ZI<\/p>\n<p>Martingales \u00e0 temps discrets : filtration, temps d\u2019arr\u00eat, th\u00e9or\u00e8me d\u2019arr\u00eat de Doob, convergence, martingales de carr\u00e9 int\u00e9grable, d\u00e9composition de Doob, variation quadratique, martingales locales.<br \/>\nMartingales \u00e0 temps continu : filtration, temps d\u2019arr\u00eat, th\u00e9or\u00e8me d\u2019arr\u00eat de Doob, variation quadratique, martingales de carr\u00e9 int\u00e9grable, martingales locales.<br \/>\nSemi-martingales \u00e0 temps continu<br \/>\nMouvement brownien : d\u00e9finition, continuit\u00e9 des trajectoires, construction, comportement des trajectoires, propri\u00e9t\u00e9 de Markov forte.<br \/>\nInt\u00e9grale stochastique : construction, in\u00e9galit\u00e9 de Kunita-Watanab\u00e9, formule d\u2019It\u00f4, applications de la formule d\u2019It\u00f4, Th\u00e9or\u00e8me de Girsanov, temps local, formule de Tanaka, changement de temps, th\u00e9or\u00e8me de repr\u00e9sentation des martingales browniennes.<br \/>\nEquations diff\u00e9rentielles stochastiques : cas Lipschitzien, propri\u00e9t\u00e9 de Markov, martingale exponentielle, condition de Novikov. <\/p>\n","protected":false},"excerpt":{"rendered":"<p>MPSAV2-Martingales, mouvement brownien et calcul stochastique Modeste N\u2019ZI Martingales \u00e0 temps discrets : filtration, temps d\u2019arr\u00eat, th\u00e9or\u00e8me d\u2019arr\u00eat de Doob, convergence, martingales de carr\u00e9 int\u00e9grable, d\u00e9composition de Doob, variation quadratique, martingales locales. Martingales \u00e0 temps continu : filtration, temps d\u2019arr\u00eat, th\u00e9or\u00e8me d\u2019arr\u00eat de Doob, variation quadratique, martingales de carr\u00e9 int\u00e9grable, martingales locales. Semi-martingales \u00e0 temps [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":["post-45","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/m2psav.master.edu-math.org\/index.php?rest_route=\/wp\/v2\/pages\/45","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/m2psav.master.edu-math.org\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/m2psav.master.edu-math.org\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/m2psav.master.edu-math.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/m2psav.master.edu-math.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=45"}],"version-history":[{"count":1,"href":"https:\/\/m2psav.master.edu-math.org\/index.php?rest_route=\/wp\/v2\/pages\/45\/revisions"}],"predecessor-version":[{"id":46,"href":"https:\/\/m2psav.master.edu-math.org\/index.php?rest_route=\/wp\/v2\/pages\/45\/revisions\/46"}],"wp:attachment":[{"href":"https:\/\/m2psav.master.edu-math.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=45"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}