Subexponential Lower Bounds for F-ergodic Markov Processes

Explore a 56-minute lecture by Dr. Miha Bresar from the University of Warwick discussing criteria for establishing lower bounds on convergence rates in f-variation of continuous-time ergodic Markov processes to their invariant measure. Learn about novel super- and submartingale conditions for Markov process functionals, and discover path-wise arguments that produce lower bounds on excursion heights and durations from bounded sets. Examine applications to elliptic diffusions and Levy-driven stochastic differential equations with polynomial/stretched exponential upper bounds, understanding how these lower bounds match known upper bounds to establish convergence rates to stationarity. Gain insights into this joint work with Aleksandar Mijatovic, which presents methods comparable to Lyapunov drift conditions for upper bounds, potentially applicable across various mathematical settings.