Malliavin–Stein method: a survey of some recent developments

Autor:	Ehsan Azmoodeh, Giovanni Peccati, Xiaochuan Yang
Jazyk:	angličtina
Rok vydání:	2021
Předmět:	limit theorems Stein’s method Malliavin calculus Wiener space Poisson space multiple integral Applied mathematics. Quantitative methods T57-57.97 Mathematics QA1-939
Zdroj:	Modern Stochastics: Theory and Applications, Vol 8, Iss 2, Pp 141-177 (2021)
Druh dokumentu:	article
ISSN:	2351-6046 2351-6054
DOI:	10.15559/21-VMSTA184
Popis:	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 generalizations in the framework of Markov semigroups and of random point measures.
Databáze:	Directory of Open Access Journals
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