Stochastic De Giorgi Iteration and Regularity of Stochastic Partial Differential Equation

Under general conditions we show that the solution of a stochastic parabolic partial differential equation of the form $\partial_t u = \mathrm{div} (A \nabla u) + f(t,x, u) + g_i (t,x,u) \dot{w}^i_t$ is almost surely Hölder continuous in both space and time variables.

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