The aim of this article is to study the asymptotic behavior for large times of solutions of linear stochastic partial differential equations of parabolic type. In particular, we will prove the backward uniqueness result and the existence of the spectral limit for abstract SPDEs and then show how...

The solution Xn to a nonlinear stochastic differential equation of the form dXn(t)+An(t)Xn(t)dt−12∑j=1N(Bjn(t))2Xn(t)dt=∑j=1NBjn(t)Xn(t)dβjn(t)+fn(t)dt, Xn(0)=x, where βjn is a regular approximation of a Brownian motion βj, Bjn(t) is a family of linear continuous operators from V to H...