Optimal Regularity for Semilinear Stochastic Partial Differential   Equations with Multiplicative Noise
  This paper deals with the spatial and temporal regularity of the unique Hilbert space valued mild solution to a semilinear stochastic partial differential equation with nonlinear terms that satisfy global Lipschitz conditions. It is shown that the mild solution has the same optimal regularity properties as the stochastic convolution. The proof is elementary and makes use of existing results on the regularity of the solution, in particular, the H\"older continuity with a non-optimal exponent. 
Raphael Kruse and Stig Larsson
math.AP math.PR