R. Mikulevicius, H. Pragarauskas, N. Sonnadara
We study the Cauchy-Dirichlet problem for a second order linear parabolic stochastic differential equation (SPDE) with constant coefficients in a half-space. Considering its solution as a function with values in a probability space and using the methods of deterministic partial differential equations, we establish the existence and uniqueness of a strong solution in Hölder classes with weights.
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