Malliavin-Stein method: a survey of some recent developments

Azmoodeh, Ehsan ORCID: 0000-0002-0401-793X, Peccati, Giovanni and Yang, Xiaochuan (2021) Malliavin-Stein method: a survey of some recent developments. MODERN STOCHASTICS-THEORY AND APPLICATIONS, 8 (2). pp. 141-177.

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Official URL: http://dx.doi.org/10.15559/21-vmsta184

Abstract

Initiated around the year 2007, the Malliavin-Stein approach to probabilistic approximations combines Stein's method with infinite-dimensional integration by parts formulae based on the use of Malliavin-type operators. In the last decade, Malliavin-Stein techniques have allowed researchers to establish new quantitative limit theorems in a variety of domains of theoretical and applied stochastic analysis. The aim of this survey is to illustrate some of the latest developments of the Malliavin-Stein method, with specific emphasis on extensions and generalisations in the framework of Markov semigroups and of random point measures.

Item Type:	Article
Additional Information:	arXiv admin note: text overlap with arXiv:1009.1310 by other authors
Uncontrolled Keywords:	Limit theorems, Stein's method, Malliavin calculus, Wiener space, Poisson space, multiple integral, Markov triple, Markov generator, eigenspace, eigenfunction, spectrum, functional Gamma-calculus, weak convergence, fourth moment theorems, Berry-Essen bounds, probability metrics
Depositing User:	Symplectic Admin
Date Deposited:	19 Dec 2022 16:11
Last Modified:	19 Dec 2022 16:11
DOI:	10.15559/21-VMSTA184
Open Access URL:	https://www.vmsta.org/journal/VMSTA/article/214/te...
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3166727