Generators of Markov Chains: From a Walk in the Interior to a Dance on the Boundary (Cambridge Studies in Advanced Mathematics, Series Number 190)

Elementary treatments of Markov chains, especially those devoted to discrete-time and finite state-space theory, leave the impression that everything is smooth and easy to understand. This exposition of the works of Kolmogorov, Feller, Chung, Kato, and other mathematical luminaries, which focuses on time-continuous chains but is not so far from being elementary itself, reminds us again that the impression is false: an infinite, but denumerable, state-space is where the fun begins. If you have not heard of Blackwell's example (in which all states are instantaneous), do not understand what the minimal process is, or do not know what happens after explosion, dive right in. But beware lest you are enchanted: 'There are more spells than your commonplace magicians ever dreamed of.'

Adam Bobrowski is a professor and Chairman of the Department of Mathematics at Lublin University of Technology, Poland. He is a pure mathematician who uses the language of operator semigroups to describe stochastic processes. He has authored and co-authored nearly 70 papers on the subject, and five books, including Functional Analysis for Probability and Stochastic Processes (2005) and Convergence of One-Parameter Operator Semigroups (2016).