Weak convergence of probability measures of Yosida approximate mild solutions of neutral SPDEs

In this paper, a neutral stochastic partial differential equation is studied in real separable Hilbert spaces. The aim here is to introduce Yosida approximations for this class of equations and to show the convergence of the mild solutions of the Yosida approximating systems in the pth-mean (p≥2) to the mild solutions of such equations. Moreover, in the special case when the neutral term has no delay, the weak convergence of probability measures induced by the mild solutions of the Yosida approximating system to the probability measures induced by mild solutions of the original equation is proved for the case p=2.