{"id":2750,"date":"2023-09-12T06:12:36","date_gmt":"2023-09-12T06:12:36","guid":{"rendered":"https:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/?page_id=2750"},"modified":"2026-11-06T16:45:12","modified_gmt":"2026-11-06T16:45:12","slug":"m2-pcs-stochastic-processes","status":"publish","type":"page","link":"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/enseignements\/enseignements-en-master\/m2-pcs-stochastic-processes\/","title":{"rendered":"M2 PCS &#8211; Stochastic processes"},"content":{"rendered":"\n<p>Lectures for the <a href=\"https:\/\/physics-complex-systems.fr\/\">master Physics of Complex Systems<\/a>, S3<\/p>\n<ul>\n<li>tuesday 8h30-12h45 : Universit\u00e9 Paris Cit\u00e9 (B\u00e2timent <span style=\"color: #999999\"><del>Condorcet, room 050A<\/del><\/span> Sophie Germain, salle 0011)<\/li>\n<li>thursday 9h00-13h15 : Universit\u00e9 Paris-Saclay (B\u00e2timent <span class=\"wdg-select-all-ok\">\u210f<\/span> n\u00b0625, amphi A6)<\/li>\n<li>first lecture the tuesday 1st september &amp; last lecture the tuesday 13th october.<\/li>\n<li>exam: <span style=\"color: #339966\">wednesday 28th october 2026<\/span><\/li>\n<\/ul>\n<h4><strong>Program:<\/strong><\/h4>\n<ol>\n<li>Few useful concepts of probability theory<\/li>\n<li>Introduction to Langevin equation<\/li>\n<li>Markov processes and Master equation<\/li>\n<li>Stochastic differential equations<\/li>\n<li>Fokker-Planck equation<\/li>\n<li>Functionals of stochastic processes<\/li>\n<\/ol>\n<h4><strong>Lecture notes<\/strong><\/h4>\n<ul>\n<li>lecture notes (<span style=\"color: #ff0000\">update : 14\/10\/26<\/span>): <span style=\"color: #999999\">cf. Moodle<\/span><\/li>\n<\/ul>\n<h4><strong>Tutorials:<\/strong><\/h4>\n<ul>\n<li>Tut n\u00b01 : Probability (1)<\/li>\n<li>Tut n\u00b02 : Probability (2)<\/li>\n<li>Tut n\u00b03 : Langevin equation<\/li>\n<li>Tut n\u00b04 : Master equation (1)<\/li>\n<li>Tut n\u00b05 : Master equation (2)<\/li>\n<li>Tut n\u00b06 : SDE (1)<\/li>\n<li>Tut n\u00b07 : SDE (2) &#8211; Application for the Anderson localization in 1D<\/li>\n<li>Tut n\u00b08 : FPE (1)<\/li>\n<li>Tut n\u00b09 : FPE (2)<\/li>\n<li>Tut n\u00b010 : FPE (3) : first passage times<\/li>\n<li>Tut n\u00b011 : Functionals<\/li>\n<\/ul>\n<h4><strong>Exams:<\/strong><\/h4>\n<ul>\n<li>december 2023 : <a href=\"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/files\/2024\/01\/sp-exam2023-12.pdf\">e<\/a>xam &amp; correction<\/li>\n<li>october 2024 : Linear drift &#8212; Conditioning in SDE &amp; <a href=\"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/files\/2024\/10\/sp-exam2024-10-corr.pdf\">c<\/a>o<a href=\"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/files\/2024\/10\/sp-exam2024-10-corr.pdf\">r<\/a>rection<\/li>\n<li>october 2025 : Wealth distribution in a m.f. model of economy &#8212; Weak quantum measurements &amp; correction<\/li>\n<li>october 2026 : Linear response within FPE &#8212; Run and tumble particle &amp; correction<\/li>\n<\/ul>\n<p><span style=\"color: #999999\">cf. Moodle<\/span><\/p>\n<h4><strong>Bibliography:<\/strong><\/h4>\n<ul>\n<li>C. W. Gardiner, <em>Handbook of stochastic methods for physics, chemistry and the natural sciences<\/em>, Springer, 1989<\/li>\n<li>H. Risken, <em>The Fokker-Planck equation<\/em>, Springer, 1989<\/li>\n<li>N. G. van Kampen, <em>Stochastic processes in physics and chemistry<\/em>, North-Holland, 1992<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Lectures for the master Physics of Complex Systems, S3 tuesday 8h30-12h45 : Universit\u00e9 Paris Cit\u00e9 (B\u00e2timent Condorcet, room 050A Sophie Germain, salle 0011) thursday 9h00-13h15 : Universit\u00e9 Paris-Saclay (B\u00e2timent \u210f n\u00b0625, amphi A6) first lecture the tuesday 1st september &amp; &hellip; <a href=\"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/enseignements\/enseignements-en-master\/m2-pcs-stochastic-processes\/\">Continuer la lecture <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":7,"featured_media":0,"parent":11,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-2750","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/wp-json\/wp\/v2\/pages\/2750","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/wp-json\/wp\/v2\/comments?post=2750"}],"version-history":[{"count":92,"href":"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/wp-json\/wp\/v2\/pages\/2750\/revisions"}],"predecessor-version":[{"id":3213,"href":"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/wp-json\/wp\/v2\/pages\/2750\/revisions\/3213"}],"up":[{"embeddable":true,"href":"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/wp-json\/wp\/v2\/pages\/11"}],"wp:attachment":[{"href":"http:\/\/www.lptms.universite-paris-saclay.fr\/christophe_texier\/wp-json\/wp\/v2\/media?parent=2750"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}