Continuity of Solutions of Diffusion SPDEs with respect to the Initial Condition and Coefficients
摘要
In this article using appropriate estimates, we prove the continuity of solutions of stochastic PDEs (SPDEs) corresponding to finite dimensional diffusions satisfying a stochastic differential equation (SDE) of Itô type. As an application we prove the existence of solutions of the same SPDEs and corresponding SDEs when the given noise is a cylindrical Brownian motion.