Malliavin-Stein Method: a Survey of Recent Developments

Ehsan Azmoodeh; Giovanni Peccati; Xiaochuan Yang

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arXiv · 1809.01912

Malliavin-Stein Method: a Survey of Recent Developments

Ehsan Azmoodeh·Giovanni Peccati·Xiaochuan Yang

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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.

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Ehsan Azmoodeh, Giovanni Peccati, Xiaochuan Yang. 2018-09-06. Malliavin-Stein Method: a Survey of Recent Developments. https://arxiv.org/abs/1809.01912

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