Probability Seminar: Yaozhong Hu

  • Date: 03/06/2013
  • Time: 15:00
Yaozhong Hu, U. Kansas

University of British Columbia


Malliavin calculus and convergence in density of some nonlinear Gaussian functionals

The classical central limit theorem is one of the most important theorem in probability theory.  The theorem states that if X_1, \cdots , X_n are independent identically distributed random variables and if F_n is the difference between the sample mean and the mean of the random variables properly normalized, then F_n converges to a normal distribution in distribution.  Recent results extend this results to other random variables for example given by Wiener chaos (multiple It\^o-Wiener integrals). In this talk, we shall obtain some conditions on F_n such that the distributions of the random variables F_n have densities f_n(x)  with respect to Lebesgue  measure and f_n(x) converges to the normal density \phi(x)=\frac{1}{\sqrt{2\pi}}e^{-|x|^2/2}.

The tool that we use is the Malliavin calculus and a brief introduction will also be given.

This is an ongoing joint work with Fei Lu and David Nualart.
Other Information: 

Location: ESB 2012