Various limiting criteria for multidimensional diffusion processes

Abstract

In this dissertation we consider several limiting criteria for n-dimensional diffusion processes defined as solutions of stochastic differential equations. Our main interest is in criteria for polynomial and exponential rates of convergence to the steady state distribution in the total variation norm. Resulting criteria should place assumptions only on the coefficients of the elliptic differential operator governing the diffusion.

Coupling of Harris chains is one of the main methods employed in this dissertation.