Statistics and Data Science Seminar
Prof. Yaozhong Hu
University of Kansas
Malliavin calculus and convergence in density of some nonlinear Gaussian functionals
Abstract: 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
Wednesday October 23, 2013 at 4:00 PM in SEO 636