Stochastic evolution equations in UMD Banach spaces
type: Item
instance of: scholarly article
title: Stochastic evolution equations in UMD Banach spaces
zbMATH Open document ID: 1149.60039
author: Jan van Neerven
author: Mark Veraar
author: Lutz Weis
published in: Journal of Functional Analysis
publication date: 2008-09-01T00:00:00Z
full work available at URL: https://arxiv.org/abs/0804.0932
review text: Let \(E\) be a UMD Banach space, \(H\) a Hilbert space, \(A\) the generator of a \(C_0\)-semigroup on \(E\), \(W_H\) a cylindrical Brownian motion on \(H\). Under Lipschitz and lineae growth conditions on \(F\) and \(B\), the existence, uniqueness and space-time regularity of solutions to the following semi-linear stochastic differential equation were addressed in the paper: \[ d U(t)= (AU(t)+F(t,U(t)))d t +B(t, U(t))d W_H(t). \]
reviewed by: Feng-Yu Wang
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 46B09
zbMATH DE Number: 5318655
zbMATH Keywords: stochastic evolution equation
zbMATH Keywords: Banach space
zbMATH Keywords: regularity
MaRDI profile type: Publication
OpenAlex ID: W2154887728
arXiv ID: 0804.0932
cites work: Q3737987
cites work: Stochastic partial differential equations in \(M\)-type 2 Banach spaces
cites work: On stochastic convolution in banach spaces and applications
cites work: Space-time regularity for linear stochastic evolution equations driven by spatially homogeneous noise
cites work: Martingales and singular integrals in Banach spaces
cites work: Q4487402
cites work: Some remarks on tangent martingale difference sequences in \(L^{1}\)-spaces
cites work: A note on stochastic convolution
cites work: Stochastic Equations in Infinite Dimensions
cites work: Regularity of solutions of linear stochastic equations in hilbert spaces
cites work: ℛ-boundedness, Fourier multipliers and problems of elliptic and parabolic type
cites work: New thoughts on old results of R. T. Seeley
cites work: Q4850055
cites work: Q3749576
cites work: Q3479287
cites work: Nonreflexive spaces of type 2
cites work: Wavelet transform for functions with values in UMD spaces
cites work: Embedding vector‐valued Besov spaces into spaces of γ ‐radonifying operators
cites work: The H∞-Functional Calculus and Square Function Estimates
cites work: The \(H^\infty\)-calculus and sums of closed operators
cites work: Eigenvalue distribution of compact operators
cites work: Q4247243
cites work: Q4657003
cites work: Q4188284
cites work: Analytic semigroups and optimal regularity in parabolic problems
cites work: Q5750044
cites work: On the continuity of Ornstein-Uhlenbeck processes in infinite dimensions
cites work: Q3375716
cites work: On the action of Lipschitz functions on vector-valued random sums
cites work: Stochastic integration of functions with values in a Banach space
cites work: Q5290219
cites work: Conditions for stochastic integrability in UMD Banach spaces
cites work: Stochastic integration in UMD Banach spaces
cites work: Q4162067
cites work: On the space of vector-valued functions integrable with respect to the white noise
cites work: Q4722940
cites work: Interpolation in $L^{p}$ with boundary conditions
cites work: Da Prato-Zabczyk's maximal inequality revisited. I.
cites work: Q3207428
cites work: Q4169288
cites work: Q4040351
cites work: Q3747436
cites work: Operator-valued Fourier multiplier theorems and maximal \(L_p\)-regularity
DOI: 10.1016/J.JFA.2008.03.015
description: scientific article