Continuity properties of Hilbert space valued martingales
type: Item
instance of: scholarly article
title: Continuity properties of Hilbert space valued martingales
zbMATH Open document ID: 0541.60052
DOI: 10.1016/0304-4149(84)90314-4
published in: Stochastic Processes and their Applications
publication date: 1984-01-01T00:00:00Z
review text: Necessary and sufficient conditions for Hölder continuity of Hilbert space valued martingales are given in terms of the associated quadratic variation. A corollary of this result is a readily verifiable sufficient condition for the sample path continuity of the mild solution of a stochastic evolution equation. Furthermore Levy's modulus of continuity and a generalized loglog law are obtained for a Hilbert space valued stochastic integral with a Wiener process integrator.
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 60G44
Mathematics Subject Classification ID: 60H15
zbMATH DE Number: 3860109
zbMATH Keywords: Hölder continuity of Hilbert space valued martingales
zbMATH Keywords: mild solution of a stochastic evolution
author: Peter M. Kotelenez
MaRDI profile type: Publication
full work available at URL: 0304-4149(84)90314-4
OpenAlex ID: W2054535963
cites work: The log log law for multidimensional stochastic integrals and diffusion processes
cites work: Infinite dimensional linear systems theory
cites work: On the path regularity of a stochastic process in a hilbert space, defined by the ito integral
cites work: Q4042404
cites work: Calcul stochastique et problèmes de martingales
cites work: Q3924934
cites work: Local behaviour of hilbert space valued stochastic integrals and the continuity of mild solutions of stochastic evolution equations
cites work: The Law of the Iterated Logarithm for Brownian Motion in a Banach Space
cites work: Q4139359
cites work: Q5585820
cites work: Q3914121
cites work: Q4187050
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description: scientific article; zbMATH DE number 3860109