Generalized Mehler semigroups: The non-Gaussian case
type: Item
instance of: scholarly article
title: Generalized Mehler semigroups: The non-Gaussian case
zbMATH Open document ID: 0957.47028
DOI: 10.1023/A:1008644017078
author: Marco Fuhrman
author: Michael Röckner
published in: Potential Analysis
publication date: 2001-03-09T00:00:00Z
review text: A generalized Mehler semigroup on a Hilbert space \(E\), acting on bounded Borel functions \(f:E\to{\mathbb R}\), is defined by the formula \[ p_t f(x) = \int_E f(T_tx+y)\mu_t(dy), \quad x\in E,\;t > 0. \] Here \((T_t)_{t\geq 0}\) is a strongly continuous semigroup of linear operators on \(E\) and \(\mu_t\) is a family of probability measures on \(E\). These semigroups were introduced by \textit{V. I. Bogachev, M. Röckner} and \textit{B. Schmuland} [Probab. Theory Relat. Fields 105, No. 2, 193-225 (1996; Zbl 0849.60066)] and studied especially in the Gaussian case. In the present paper the authors consider the general, non-Gaussian case. In particular, an associated Markov process is constructed, tightness of the associated \((r,p)\)-capacities is proved. Moreover, existence of invariant measures, strong Feller property, time regularity in the space of uniformly continuous and bounded functions, and description of the generator are also studied.
reviewed by: Michael Perelmuter
Mathematics Subject Classification ID: 47D07
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 1436912
zbMATH Keywords: generalized Mehler semigroup
zbMATH Keywords: non-Gaussian
zbMATH Keywords: Markov process
zbMATH Keywords: tightness
zbMATH Keywords: invariant measures
zbMATH Keywords: strong Feller property
zbMATH Keywords: regularity
MaRDI profile type: Publication
full work available at URL: a:1008644017078
OpenAlex ID: W2177262980
description: scientific article; zbMATH DE number 1436912