Stochastic evolution equations with fractional Brownian motion
type: Item
instance of: scholarly article
title: Stochastic evolution equations with fractional Brownian motion
zbMATH Open document ID: 1036.60056
publication date: 2003-12-16T00:00:00Z
review text: The authors consider the equation \[ X(dt)=AX(t)\,dt+\Phi \,dB^H_t. \] Here \(B^H_t\) is infinite-dimensional fractional Brownian motion, \(A\) is an unbounded linear operator and \(\Phi\) is a bounded linear operator in the corresponding Hilbert space. The main theorems give conditions for the existence of the so-called mild solution, i.e. for \[ X(t)=e^{tA}x+\int _0^te^{(t-s)A}\Phi \,dB^H(s), \] and for the regularity of this solution. Regularity now means that \(X(t)\) belongs to the domain of definition of \((-A)^\gamma\) and is continuous in the corresponding norm. The authors use the integral representation of the fractional Brownian motion with the help of Wiener process and estimate the integral kernel for \(X.\)
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 60G15
zbMATH DE Number: 2018319
zbMATH Keywords: fractional Brownian motion
zbMATH Keywords: evolution equation
zbMATH Keywords: mild solution
author: S. Tindel
author: Ciprian A. Tudor
author: Frederi Viens
reviewed by: A. A. Dorogovtsev
MaRDI profile type: Publication
full work available at URL: s00440-003-0282-2
OpenAlex ID: W1966589369
DOI: 10.1007/S00440-003-0282-2
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
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description: scientific article; zbMATH DE number 2018319