Uniform mixing bounds for SDE approximations via Harnack inequality and Malliavin calculus

Alexander Veretennikov (University of Leeds)

(joint work with S.A.Klokov)

Two kinds of SDE approximations in $R^d$ are considered, with Gaussian and non-Gaussian noise, the latter case requires a `good density'. The theoretical question under consideration is establishing a priori bounds for convergence to equilibrium and beta-mixing uniformly with respect to time step size of approximations. Convergence to limiting SDEs is not used, nor it is established. In various cases and for various approaches, various standing assumptions are required related to smoothness of SDE coefficients and noise density, from just boundedness to several derivatives and existence of Fisher's information. In the non-Gaussian case diffusion coefficient is assumed to be constant and non-degenerate. Two main methods used in this work are Harnack's inequality and stochastic calculus of variations.