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Poisson random measures, Lévy processes, generalized stochastic calculus, continuous state branching processes
发布时间: 2017-10-13     10:22   【返回上一页】 发布人:Etienne Pardoux教授


 

北京师范大学数学科学学院

概率论短期课程

 

课程名称:Poisson random measures, Lévy processes, generalized stochastic calculus, continuous state branching processes

 

主讲人:Etienne Pardoux教授, 法国Aix-Marseille大学

 

说明: D:/0Seagate01/lizh0docs/3Activities/171015Students/Pardoux2015b.jpg

 

课程简介:

The Poisson distribution appears very naturally as the law of a random cloud of points, under mild conditions. We will define and study Poisson Random measures of points. We shall then show how to use them in order to define all Lévy processes other than the Brownian motion. This requires defining stochastic integrals of deterministic functions with respect to a compensated Poisson random measure. We shall also integrate predictable random processes, establish a generalized Itô formula, solve SDEs directed by a Lévy process, and prove the Markov property of the solution. Finally we shall study Dawson-Li type SDEs, whose solutions are general continuous state branching processes. We shall see that the Lamperti transform changes those into Lévy processes. 

 

地点:后主楼1124

 

时间:

1016日下午15:30-17:301018日下午14:00-17:001020日上午8:40-11:401022日上午8:40-11:40

 

主讲人简介:Pardoux教授是国际知名随机分析专家,与彭实戈院士同为倒向随机微分方程理论的奠基人。他与Mattingly的工作是HairerMattingly关于二维随机Navier-Stokes方程遍历性工作的重要基础,后者是2014HairerFields奖的两项主要工作之一。