[{"command":"insert","method":null,"selector":".course-modal-ajax-placeholder-968259","data":"\u003Cdiv class=\u0022container content-rte\u0022\u003E\n  \u003Cdiv class=\u0022row\u0022\u003E\n    \u003Cdiv class=\u0022box col-md-6 bg-primary text-white\u0022\u003E\n      \u003Ch2 class=\u0022h1 text-left\u0022\u003E  Processus stochastiques\n\u003C\/h2\u003E\n                  \u003Cdiv class=\u0022field-spacing\u0022\u003E\n        \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EECTS :\n          4\n        \u003C\/div\u003E\n      \u003C\/div\u003E\n                  \u003Cdiv class=\u0022field-spacing\u0022\u003E\n        \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ESemestre calendaire :\n          Semester 1\n        \u003C\/div\u003E\n      \u003C\/div\u003E\n            \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ED\u00e9tail du volume horaire\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                          \u003Cspan class=\u0022field__label h4 mt-5 \u0022\u003ECours magistraux :\u003C\/span\u003E\n                                      \u003Cspan\u003E21\u003C\/span\u003E\n                      \u003C\/div\u003E\n                                              \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                          \u003Cspan class=\u0022field__label h4 mt-5 \u0022\u003ETravaux dirig\u00e9s :\u003C\/span\u003E\n                                      \u003Cspan\u003E21\u003C\/span\u003E\n                      \u003C\/div\u003E\n                                                            \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ELangue d\u0026#039;enseignement\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003EAnglais\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EEnseignement \u00e0 distance\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003Enon\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n      \u003C\/div\u003E\n    \u003Cdiv class=\u0022box col-md-6\u0022\u003E\n            \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EPr\u00e9requis\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003EProbability theory and Data analysis\u003C\/p\u003E\n\u003Cp\u003ENotions de probabilit\u00e9s et d\u2019analyse de donn\u00e9es\u003C\/p\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EProgramme \/ plan \/ contenus\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003EEn Fran\u00e7ais :\u003C\/p\u003E\n\u003Col\u003E\n\u003Cli\u003E\n\u003Cp\u003EIntroduction\u003C\/p\u003E\n\u003C\/li\u003E\n\u003Cli\u003E\n\u003Cp\u003EMartingales\na) Esperance conditionnelle\nb) D\u00e9finition de martingale et propri\u00e9t\u00e9s de base\nc) Strat\u00e9gies admissibles, temps d\u2019arr\u00eat\nd) Applications\ne) Convergence\u003C\/p\u003E\n\u003C\/li\u003E\n\u003Cli\u003E\n\u003Cp\u003ECha\u00eenes de Markov\na) Matrice de transition\nb) Classification des \u00e9tats\nc) Loi stationnaire\nd) Comportement limite\ne) Temps de passage\nf) Espaces d\u2019\u00e9tat infinis.\u003C\/p\u003E\n\u003C\/li\u003E\n\u003C\/ol\u003E\n\u003Cp\u003EIn English:\u003C\/p\u003E\n\u003Col\u003E\n\u003Cli\u003E\n\u003Cp\u003EIntroduction\u003C\/p\u003E\n\u003C\/li\u003E\n\u003Cli\u003E\n\u003Cp\u003EMartingales\na) Conditional expectation\nb) Definition of martingale and basic properties\nc) Gambling strategies, Stopping times\nd) Applications\ne) Convergence\u003C\/p\u003E\n\u003C\/li\u003E\n\u003Cli\u003E\n\u003Cp\u003EMarkov chains\na) Transition probability matrix\nb) Classification of States\nc) Stationary distributions\nd) Limit Behavior\ne) Exit times\nf) Infinite state spaces\u003C\/p\u003E\n\u003C\/li\u003E\n\u003C\/ol\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EObjectifs d\u0026#039;apprentissage\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003EEn Fran\u00e7ais :\u003C\/p\u003E\n\u003Cul\u003E\n\u003Cli\u003EInitier les \u00e9l\u00e8ves \u00e0 la notion de processus stochastiques, en particulier aux Martingales et Cha\u00eenes de Markov.\u003C\/li\u003E\n\u003Cli\u003EDonner aux \u00e9l\u00e8ves les outils n\u00e9cessaires pour comprendre les fondements et les m\u00e9thodes d\u2019analyse des processus stochastiques dans divers domaines des maths appliqu\u00e9es, notamment, en \u00e9conom\u00e9trie, en biomath\u00e9matique et en maths financi\u00e8res.\u003C\/li\u003E\n\u003C\/ul\u003E\n\u003Cp\u003EIn English:\u003C\/p\u003E\n\u003Cul\u003E\n\u003Cli\u003EIntroduce the students to the concept of stochastic processes and in particular to the notions of Martingales and Markov chains.\u003C\/li\u003E\n\u003Cli\u003EProvide the students the tools necessary to understand the foundations of stochastic processes and the methods to analyse them in multiple domains of applied maths, including econometrics, and mathematical biology and finance.\u003C\/li\u003E\n\u003C\/ul\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EOrganisation g\u00e9n\u00e9rale et modalit\u00e9s p\u00e9dagogiques\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003EEn Fran\u00e7ais :\nEvaluation : 1 Partiel + 1 TP not\u00e9 (40%) 1 Examen final (60%) D\u00e9coupage : 14 s\u00e9ances cours, 8 s\u00e9ances TD, 2 s\u00e9ances TP.\u003C\/p\u003E\n\u003Cp\u003EIn English:\u003C\/p\u003E\n\u003Cp\u003EGrading: 1 midterm + 1 computer-based exam (40%) 1 final exam (60%) Schedule: 14 class sessions, 8 tutorial class sessions, 2 computer-based tutorials.\u003C\/p\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n                        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EBibliographie\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003ER. Durrett. Essentials of stochastic processes. Springer, 2016.\u003C\/p\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ENature de l\u0026#039;\u00e9valuation\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003EEvaluation Continue non Int\u00e9grale\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n      \u003C\/div\u003E\n  \u003C\/div\u003E\n\u003C\/div\u003E\n","settings":null}]