Markov Chains on Metric Spaces

This book gives an introduction to discrete-time Markov chains which evolve on a separable metric space. 

The focus is on the ergodic properties of such chains, i.e., on their long-term statistical behaviour. Among the main topics are existence and uniqueness of invariant probability measures, irreducibility, recurrence, regularizing properties for Markov kernels, and convergence to equilibrium. Th...