This paper revisits the Hölder regularity of mild solutions of parabolic stochastic Cauchy problems in Lebesgue spaces Lp(O), with p ≥ 2 and O ⊂ ℝd a bounded domain. We find conditions on p,β and γ under which the mild solution has almost surely trajectories in Cβ([0,T ]; Cγ (Ō). 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 Brzeźniak (Stochastics Stochastics Rep. 61 (1997) 245–295).
|Original language||English (US)|
|Number of pages||11|
|Journal||Brazilian Journal of Probability and Statistics|
|State||Published - Nov 1 2015|
All Science Journal Classification (ASJC) codes
- Statistics and Probability