Abstract

In this paper we use regularization methods for proving the existence and uniqueness of smooth solutions of a first order semilinear stochastic partial differential equation. The regularizations are chosen in such a way so that the known theory of stochastich parabolic Ito equations can be applied. The existence of the generalized solutions and, if the the time parameter is the whole real axis, the existence of mean square bounded generalized solutions, is also considered

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