Title:  Multidimensional normal approximation by Stein's method and Bismut formula

Speaker: Dr.  Lihu Xu (徐礼虎),   澳门大学

Time:  3:00pm,  2018-12-21

Location:   200-9 The 2^th Floor, Sir R. R. Shaw Building,

Yuquan Campus, Zhejiang University

Abstract: Stein's method has been widely used for probability approximations. However, in the multi-dimensional setting, most of the results are for multivariate normal approximation or for test functions with bounded second- or higher-order derivatives. For a class of multivariate limiting distributions, we use Bismut's formula in Malliavin calculus to control the derivatives of the Stein equation solutions by the first derivative of the test function.Combined with Stein's exchangeable pair approach, we obtain a general theorem for multivariate approximations with near optimal error bounds on the Wasserstein distance. We apply the theorem to the unadjusted Langevin algorithm.

All are welcome!

Contact Person: Zhonggen Su,  suzhonggen@zju.edu.cn

浙江大学统计研究所

2018-12-10