We prove existence and (in some special case) uniqueness of an invariant measure for the transition semigroup associated with the stochastic wave equations with nonlinear dissipative damping.

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...

We prove the existence of an invariant measure [mu] for the transition semigroup Pt associated with the fast diffusion porous media equation in a bounded domain , perturbed by a Gaussian noise. The Kolmogorov infinitesimal generator N of Pt in is characterized as the closure of a second-order...

Exit from a neighborhood of zero for weakly damped stochasticnonlinear SchrÄodinger equations is studied. The small noise is either complexand of additive type or real and of multiplicative type. It is white in time andcolored in space. The neighborhood is either in L2 or in H1. The small...

In this paper we study ergodic backward stochastic differential equations (EBSDEs) dropping the strong dissipativity assumption needed in Fuhrman et al. (2009) [12]. In other words we do not need to require the uniform exponential decay of the difference of two solutions of the underlying...