Probability Theory IV

This volume of the EMS gives a comprehensive account of all the main topics in the theory of Markov processes. The authors Portenko, Skorokhod and Shurenkov are among the leading authorities on the theory of stochastic processes. After starting with the basic definitions and motivating examples the authors give careful attention to the theory of diffusion processes and their connections with partial differential equations and stochastic differential equations. Other topics are homogeneous Markov processes and finally, the authors discuss ergodic theory. Here they give an elegant account of theorems on the law of large numbers, statements on the existence of limits of position probabilities, and "integral" limit theorems for ratios. Readers should appreciate a book which treats all the important topics including recent advances in the field of Markov processes in one volume. Graduate students and researchers in the theory of stochastic processes should find this volume of EMS immensely useful.