I will discuss some techniques used in investigating the existence, uniqueness and asymptotics of stationary distributions for diffusion processes on non-compact spaces that arise in several physical models. These problems are more challenging when the driving noise is low dimensional (hypoelliptic diffusions). In the first talk, I will discuss couplings, which are extremely useful in estimating rates of convergence to stationarity.

You can find the slides to the talk here: talk slides

In the next talk, I plan to discuss how renewal theory can be effectively used in studying steady states of some hypoelliptic Markov processes of inert drift type that arise in physics and queueing theory.