Multi-dimensional normal approximation of heavy-tailed moving averages

Azmoodeh, Ehsan ORCID: 0000-0002-0401-793X, Ljungdahl, Mathias Morck and Thaele, Christoph (2022) Multi-dimensional normal approximation of heavy-tailed moving averages. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 145. pp. 308-334.

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Official URL: http://dx.doi.org/10.1016/j.spa.2021.11.011

Abstract

In this paper we extend the refined second-order Poincar\'e inequality for Poisson functionals from a one-dimensional to a multi-dimensional setting. Its proof is based on a multivariate version of the Malliavin-Stein method for normal approximation on Poisson spaces. We also present an application to partial sums of vector-valued functionals of heavy-tailed moving averages. The extension allows a functional with multivariate arguments, i.e. multiple moving averages and also multivariate values of the functional. Such a set-up has previously not been explored in the framework of stable moving average processes. It can potentially capture probabilistic properties which cannot be described solely by the one-dimensional marginals, but instead require the joint distribution.

Item Type:	Article
Uncontrolled Keywords:	Central limit theorem, Heavy-tailed moving average, Levy process, Malliavin-Stein method, Poisson random measure, Second-order Poincare inequality
Divisions:	Faculty of Science and Engineering > School of Physical Sciences
Depositing User:	Symplectic Admin
Date Deposited:	27 Jul 2022 14:27
Last Modified:	13 Mar 2023 22:57
DOI:	10.1016/j.spa.2021.11.011
Open Access URL:	https://arxiv.org/abs/2002.11335v3
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3078472