  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.

Probability;Functional Analysis