Markov Chains

A long time ago I started writing a book about Markov chains, Brownian motion, and diffusion. I soon had two hundred pages of manuscript and my publisher was enthusiastic. Some years and several drafts later, I had a thousand pages of manuscript, and my publisher was less enthusiastic. So we made it a trilogy: Markov Chains Brownian Motion and Diffusion Approximating Countable Markov Chains familiarly - MC, B & D, and ACM. I wrote the first two books for beginning graduate students with some knowledge of probability; if you can follow Sections 10.4 to 10.9 of Markov Chains you're in. The first two books are quite independent of one another, and completely independent of the third. This last book is a monograph which explains one way to think about chains with instantaneous states. The results in it are supposed to be new, except where there are specific disclaim­ ers; it's written in the framework of Markov Chains. Most of the proofs in the trilogy are new, and I tried hard to make them explicit. The old ones were often elegant, but I seldom saw what made them go. With my own, I can sometimes show you why things work. And, as I will VB1 PREFACE argue in a minute, my demonstrations are easier technically. If I wrote them down well enough, you may come to agree. Front Matter....Pages i-xiv Introduction to Discrete Time....Pages 1-46 Ratio Limit Theorems....Pages 47-81 Some Invariance Principles....Pages 82-110 The Boundary....Pages 111-137 Introduction to Continuous Time....Pages 138-171 Examples for the Stable Case....Pages 172-215 The Stable Case....Pages 216-251 More Examples for the Stable Case....Pages 252-296 The General Case....Pages 297-328 Appendix....Pages 329-366 Back Matter....Pages 367-382