14 research outputs found
Estimates for the ergodic measure and polynomial stability of plane stochastic curve shortening flow
We establish moment estimates for the invariant measure of a stochastic
partial differential equation describing motion by mean curvature flow in (1+1)
dimension, leading to polynomial stability of the associated Markov semigroup.
We also prove maximal dissipativity for the related Kolmogorov operator
Invariant measures for monotone SPDE's with multiplicative noise term
We study diffusion processes corresponding to infinite dimensional semilinear
stochastic differential equations with local Lipschitz drift term and an
arbitrary Lipschitz diffusion coefficient. We prove tightness and the Feller
property of the solution to show existence of an invariant measure. As an
application we discuss stochastic reaction diffusion equations.Comment: 10 page
Stationary distributions for retarded stochastic differential equations without dissipativity
In this paper, we use variation of constants formula to investigate the stationary distribution for stochastic differential delay equations. Under certain conditions (without dissipative conditions) we prove the existence and uniqueness for stochastic differential delay equations