Uniqueness of invariant measures of infinite dimensional stochastic differential equations driven by Lévy noises
type: Item
instance of: scholarly article
title: Uniqueness of invariant measures of infinite dimensional stochastic differential equations driven by Lévy noises
zbMATH Open document ID: 1260.60126
author: Bin Xie
published in: Potential Analysis
publication date: 2012-01-12T00:00:00Z
review text: The author investigates uniqueness of invariant measures for stochastic differential equation driven by a Lévy type noise in a real separable Hilbert space. A non-degeneracy condition on the coefficient of the Wiener process is assumed. Uniqueness of invariant measures is established by proving both strong Feller property and irreducibility of the corresponding Markov transition semigroup. In particular, the strong Feller property is based on a Bismut-Elworthy-Li type formula in infinite dimensions. A related Bismut-Elworthy-Li type formula has been recently proved by \textit{C. Marinelli, C. Prévôt} and \textit{M. Röckner} [J. Funct. Anal. 258, No. 2, 616--649 (2010; Zbl 1186.60060)].
reviewed by: E. Priola
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 60J75
Mathematics Subject Classification ID: 60J99
Mathematics Subject Classification ID: 37H10
zbMATH DE Number: 5996884
zbMATH Keywords: uniqueness of invariant measure
zbMATH Keywords: Lévy noise
zbMATH Keywords: Bismut-Elworthy-Li type formula
zbMATH Keywords: strong Feller
zbMATH Keywords: irreducibility
MaRDI profile type: Publication
full work available at URL: s11118-011-9220-6
OpenAlex ID: W2016887541
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DOI: 10.1007/S11118-011-9220-6
description: scientific article; zbMATH DE number 5996884