Kolmogorov equation associated to the stochastic reflection problem on a smooth convex set of a Hilbert space

We consider the stochastic reflection problem associated with a self-adjoint operator $A$ and a cylindrical Wiener process on a convex set $K$ with nonempty interior and regular boundary $\Sigma$ in a Hilbert space $H$. We prove the existence and uniqueness of a smooth solution for the corresponding elliptic infinite-dimensional Kolmogorov equation with Neumann boundary condition on $\Sigma$.Comment: Published in at http://dx.doi.org/10.1214/08-AOP438 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Coupling for some partial differential equations driven by white noise

We prove, using coupling arguments, exponential convergence to equilibrium for reaction--diffusion and Burgers equations driven by space-time white noise. We use a coupling by reflection

Surface measures in infinite dimension

We construct surface measures associated to Gaussian measures in separable Banach spaces, and we prove several properties including an integration by parts formula

Green and Poisson Functions with Wentzell Boundary Conditions

We discuss the construction and estimates of the Green and Poisson functions associated with a parabolic second order integro-di erential operator with Wentzell boundary conditions