Local behaviour of hilbert space valued stochastic integrals and the continuity of mild solutions of stochastic evolution equations
作者:
Peter Kotelenez,
Ruth F. Curtain,
期刊:
Stochastics
(Taylor Available online 1982)
卷期:
Volume 6,
issue 3-4
页码: 239-257
ISSN:0090-9491
年代: 1982
DOI:10.1080/17442508208833206
出版商: Gordon and Breach Science Publishers Inc
数据来源: Taylor
摘要:
Levy's modulus of continuity is proved for infinite dimensional Wiener processes. Using the loglog law for a Banach space valued Wiener process in [7], we prove the loglog law for Hilbert space valued stochastic integrals, if the integrand is Holder continuous. From a corollary of Kolmogorov's law we derive the Hölder continuity of Hilbert space valued stochastic integrals if the fourth moment of the integrand is uniformly bounded. As an application we show that the mild solution of a stochastic evolution equation has a continuous version if the semigroup governing this equation is analytic.
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