报告人：翟建梁
报告地点：腾讯会议ID：913 301 286
报告时间：2021年11月18日星期四09:00-10:00
报告摘要：
We consider McKean-Vlasov stochastic differential equations (MVSDEs) driven by Levy noise. By identifying the right equations satisfied by the solutions of the MVSDEs with shifted driving Levy noise, we build up a framework to fully apply the weak convergence method to establish large and moderate deviation principles for MVSDEs. In the case of ordinary SDEs, the rate function is calculated by using the solutions of the corresponding skeleton equations simply replacing the noise by the elements of the Cameron-Martin space. It turns out that the correct rate function for MVSDEs is defined through the solutions of skeleton equations replacing the noise by smooth functions and replacing the distributions involved in the equation by the distribution of the solution of the corresponding deterministic equation(without the noise). This is somehow surprising.With this approach, we obtain large and moderate deviation principles for much wider classes of MVSDEs in comparison with the existing literature. This talk is based on a joint work with Wei Liu, Yulin Song, Tusheng Zhang
主讲人简介：
翟建梁副教授于2010年获中国科学院数学与系统科学研究院理学博士，2010年进入北京博士后流动站，现为中国科学技术大学副教授。主要研究方向是Levy过程驱动的随机偏微分方程，最近几年也对随机动力系统方向很感兴趣。已发表论文20余篇, 包括“J. Funct. Anal.”、“Bernoulli”、”“J. Differential Equations”、“J. Math. Pures Appl.”等国际重要杂志。主要学术贡献：Levy过程驱动的随机偏微分方程的鞅解存在性和马氏选择、时间正则性、大偏差原理、中偏差原理等；平稳测度支撑的渐近行为的研究。主持国家自然科学基金青年基金、面上项目各一项，参加国家自然科学基金重点项目一项。
