Total variation distance between stochastic polynomials and invariance principles
Abstract
The goal of this paper is to estimate the total variation distance between two general stochastic polynomials. As a consequence, one obtains an in-variance principle for such polynomials. This generalizes known results concerning the total variation distance between two multiple stochastic integrals on one hand, and invariance principles in Kolmogorov distance for multilin-ear stochastic polynomials on the other hand. As an application, we first discuss the asymptotic behavior of U-statistics associated to polynomial kernels. Moreover, we also give an example of CLT associated to quadratic forms.