TOTAL VARIATION DISTANCE BETWEEN STOCHASTIC POLYNOMIALS AND INVARIANCE PRINCIPLES

• 成果类型: Article
• 署名作者: Bally, Vlad; Caramellino, Lucia
• 署名单位: Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Centre National de la Recherche Scientifique (CNRS); University of Rome Tor Vergata; University of Rome Tor Vergata
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/19-AOP1346
• 发表日期: 2019
• 页码: 3762-3811
• 关键词: CENTRAL LIMIT-THEOREMS; UNIVERSALITY; SEQUENCES

摘要

The goal of this paper is to estimate the total variation distance between two general stochastic polynomials. As a consequence, one obtains an invariance 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 multilinear 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.