Using stochastic comparison to estimate Green's functions
A variational formula for positive functionals of a Poisson random measure and brownian motion is proved. The formula is based on the relative entropy representation for exponential integrals, and can be used to prove large deviation type estimates. A general large deviation result is proved, and illustrated with an example.
A theorem on continuous dependence of solutions to stochastic evolution equations on coefficients is established, covering the classical averaging procedure for stochastic parabolic equations with rapidly oscillating both the drift and the diffusion term.
In this paper, we consider weak solutions to stochastic inclusions driven by a semimartingale and a martingale problem formulated for such inclusions. Using this we analyze compactness of the set of solutions. The paper extends some earlier results known for stochastic differential inclusions driven by a diffusion process.
We consider the linear Schrödinger equation under periodic boundary conditions, driven by a random force and damped by a quasilinear damping: The force is white in time and smooth in ; the potential is typical. We are concerned with the limiting, as , behaviour of solutions on long time-intervals , and with behaviour of these solutions under the double limit and . We show that these two limiting behaviours may be described in terms of solutions for thesystem of effective equations for(...