Annals of Probability

Total variation distance between stochastic polynomials and invariance principles

Vlad Bally and Lucia Caramellino

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Abstract

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.

Article information

Source
Ann. Probab., Volume 47, Number 6 (2019), 3762-3811.

Dates
Received: May 2017
Revised: June 2018
First available in Project Euclid: 2 December 2019

Permanent link to this document
https://projecteuclid.org/euclid.aop/1575277341

Digital Object Identifier
doi:10.1214/19-AOP1346

Mathematical Reviews number (MathSciNet)
MR4038042

Zentralblatt MATH identifier
07212171

Subjects
Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 60H07: Stochastic calculus of variations and the Malliavin calculus

Keywords
Stochastic polynomials invariance principles U-statistics quadratic central limit theorem abstract Malliavin calculus

Citation

Bally, Vlad; Caramellino, Lucia. Total variation distance between stochastic polynomials and invariance principles. Ann. Probab. 47 (2019), no. 6, 3762--3811. doi:10.1214/19-AOP1346. https://projecteuclid.org/euclid.aop/1575277341


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