A note on space–time Hölder regularity of mild solutions to stochastic cauchy problems in Lp-spaces (2015)
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.