Stochastic partial differential equations in \(M\)-type 2 Banach spaces
type: Item
instance of: scholarly article
title: Stochastic partial differential equations in \(M\)-type 2 Banach spaces
zbMATH Open document ID: 0831.35161
DOI: 10.1007/BF01048965
author: Zdzislaw Brzezniak
published in: Potential Analysis
publication date: 1995-02-16T00:00:00Z
review text: The author proves an existence and uniqueness theorem for a stochastic differential equation in \(M\)-type 2 Banach spaces of the following type \[ du(t) + Au(t)dt = \sum B^j u(t) dw^j(t) + f(t), \quad u(0) = u_0, \] where \(- A\) is a generator of an analytic semigroup \(\{e^{- tA}\}_{r \geq 0}\) on \(X\), an \(M\)-type 2 Banach space, \(B^1, \ldots, B^d\) are linear operators in \(X\) and \(w(t)\) is a \(d\)-dimensional Wiener process. The author considers the case, when the space of initial conditions is some real interpolation space between the domain of \(A\) and \(X\), and the case, when the space of initial conditions is \(X\). Also the author considers the case, when \(X\) is a Hilbert space and applies the obtained results to stochastic parabolic equations.
Mathematics Subject Classification ID: 35R60
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 47D06
zbMATH DE Number: 723919
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: space of initial conditions
zbMATH Keywords: stochastic parabolic equations
reviewed by: Aleksandr D. Borisenko
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01048965
OpenAlex ID: W2116985390
description: scientific article; zbMATH DE number 723919