Trotter-Kato approximations of semilinear stochastic evolution equations in Hilbert spaces

Abstract: Motivated by the work of T.E. Govindan in [5,8,9], this paper is concerned with a more general semilinear stochastic evolution equation. The difference between the equations considered in this paper and the previous one is that it makes some changes to the nonlinear function in random integral, which also depends on the probability distribution of stochastic process at that time. First, this paper considers the existence and uniqueness of mild solutions for such equations. Furthermore, Trotter-Kato approximation system is introduced for the mild solutions, and the weak convergence of induced probability measures and zeroth-order approximations are obtained. Then we consider the classical limit theorem about the parameter dependence of this kind of equations. Finally, an example of stochastic partial differential equation is given to illustrate our results.