A note on space-time Holder regularity of mild solutions to stochastic Cauchy problems in Lp-spaces

2014/04/30 by Rafael Serrano, Serrano, Rafael
Economics, Econometrics and Finance · Mathematics · #35R15 #Advanced Harmonic Analysis Research #FOS: Mathematics #Nonlinear Partial Differential Equations #Primary 60H15 #Probability (math.PR) #Stochastic processes and financial applications #math.PR #msc:35R15 #msc:47D06 #msc:60H15 #secondary 47D06

paper · pdf · doi:10.48550/arxiv.1405.0075

openalex publication_date 2014/04/30 · arxiv created 2014/05/01 · arxiv updated 2014/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper revisits the Hölder regularity of mild solutions of parabolic stochastic Cauchy problems in Lebesgue spaces L^p(O), with p≥ 2 and O⊂ℝ^d a bounded domain. We find conditions on p, β and γ under which the mild solution has almost surely trajectories in C^β([0,T];C^γ(O)). 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 Z. Brzeźniak (Stoch. Stoch. Rep. Vol. 61, Iss. 3-4, 1997).

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