From the reviews of the First Edition: "This excellent book is based on several sets of lecture notes written over a decade and has its origin in a one-semester

The present volume contains the most advanced theories on the martingale approach to central limit theorems. Using the time symmetry properties of the Markov pr

This book gives a comprehensive and self-contained introduction to the theory of symmetric Markov processes and symmetric quasi-regular Dirichlet forms. In a de

Markov processes are among the most important stochastic processes for both theory and applications. This book develops the general theory of these processes, a