ABSTRACT
This chapter studies stochastic partial differential equations of parabolic type, or simply, stochastic parabolic equations in a bounded domain. It presents some basic facts concerning the elliptic operator and define the Wiener random field and the related stochastic integrals. The chapter solves the heat equation driven by a spatially dependent white noise by the method of eigenfunctions expansion. The results of the solutions are generalized to study the linear parabolic equations with additive white noise. The chapter investigates the regularity properties of the solutions and treats the existence, uniqueness and the regularity questions for linear and semilinear stochastic parabolic equations.
