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


  • Brazilian Journal of Probability and Statistics


  • 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).

publication date

  • 2015-11-1


  • 29


  • Banach space
  • Bounded Domain
  • Cauchy Problem
  • Convolution
  • Hilbert space
  • Lebesgue Space
  • Lp Spaces
  • Mild Solution
  • Regularity
  • Space-time
  • Trajectory

International Standard Serial Number (ISSN)

  • 0103-0752

number of pages

  • 11

start page

  • 767

end page

  • 777