Perturbations of generalized Mehler semigroups and applications to stochastic heat equations with Levy noise and singular drift
type: Item
instance of: scholarly article
title: Perturbations of generalized Mehler semigroups and applications to stochastic heat equations with Levy noise and singular drift
zbMATH Open document ID: 1052.47033
DOI: 10.1023/B:POTA.0000009814.54278.34
author: Paul Lescot
author: Michael Röckner
published in: Potential Analysis
publication date: 2004-03-15T00:00:00Z
review text: The authors study the stochastic differential equation \(dX_t=AX_t dt+b(X_t) dt+dY_t\) on a Hilbert space \(E\), where \((Y_t)_{t\geq 0}\) is a Levy process on \(E\), \(A\) generates a \(C_0\)-semigroup on \(E\) and \(b:E\to E\) is a singular drift. Using the perturbation theory of \(C_0\)-semigroups (applied to generalized Mehler semigroups), the authors construct a strong Markov process solving the above equation in the sense of martingal problem. Under some constraint, the uniqueness in the sense of Markov selections is proved as well. An application to stochastic heat equations with Levy noise and singular drift is included.
Mathematics Subject Classification ID: 47D03
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 47D07
zbMATH DE Number: 2057484
zbMATH Keywords: generalized Mehler semigroups
zbMATH Keywords: perturbation theory
zbMATH Keywords: stochastic heat equations
reviewed by: Michael Perelmuter
MaRDI profile type: Publication
full work available at URL: b:pota.0000009814.54278.34
OpenAlex ID: W2051096020
description: scientific article; zbMATH DE number 2057484