Generators of Markov Chains: From a Walk in the Interior to a Dance on the Boundary

Cambridge Studies in Advanced Mathematics #190

by Adam Bobrowski

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 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 'There are more spells than your commonplace magicians ever dreamed of.'

278 pages, Kindle Edition

Published November 26, 2020