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A note on space–time Hölder regularity of mild solutions to stochastic cauchy problems in Lp-spaces


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Fecha
2015

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Brazilian Statistical Association

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Resumen
Abstract
This paper revisits the Hölder regularity of mild solutions of parabolic stochastic Cauchy problems in Lebesgue spaces Lp(O), with p ? 2 and O ? ?d a bounded domain. We find conditions on p,? and ? under which the mild solution has almost surely trajectories in C?([0,T ]; C? (?). These conditions do not depend on the Cameron–Martin Hilbert space associated with the driving cylindrical noise. The main tool of this study is a regularity result for stochastic convolutions in M-type 2 Banach spaces by Brze?niak (Stochastics Stochastics Rep. 61 (1997) 245–295). © Brazilian Statistical Association, 2015.
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Keywords
Additive cylindrical noise , Hölder regularity , Lebesgue spaces , Stochastic cauchy problem , Stochastic convolution
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https://www.scopus.com/inward/record.uri?eid=2-s2.0-84941932359&doi=10.1214%2f14-BJPS245&partnerID=40&md5=1b06469e6e2828ad26f8d9446dd6a23c
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