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November 2019 Total variation distance between stochastic polynomials and invariance principles
Vlad Bally, Lucia Caramellino
Ann. Probab. 47(6): 3762-3811 (November 2019). DOI: 10.1214/19-AOP1346

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.

Citation

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Vlad Bally. Lucia Caramellino. "Total variation distance between stochastic polynomials and invariance principles." Ann. Probab. 47 (6) 3762 - 3811, November 2019. https://doi.org/10.1214/19-AOP1346

Information

Received: 1 May 2017; Revised: 1 June 2018; Published: November 2019
First available in Project Euclid: 2 December 2019

zbMATH: 07212171
MathSciNet: MR4038042
Digital Object Identifier: 10.1214/19-AOP1346

Subjects:
Primary: 60F17
Secondary: 60H07

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.47 • No. 6 • November 2019
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