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AuthorFreedman, David. author
TitleMarkov Chains [electronic resource] / by David Freedman
ImprintNew York, NY : Springer New York, 1983
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Descript 382 p. online resource


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 disclaimยญ 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


I. Discrete time -- 1. Introduction to Discrete Time -- 2. Ratio Limit Theorems -- 3. Some Invariance Principles -- 4. The Boundary -- II. Continuous time -- 5. Introduction to Continuous Time -- 6. Examples for the Stable Case -- 7. The Stable Case -- 8. More Examples for the Stable Case -- 9. The General Case -- III. -- 10. Appendix -- Symbol Finder

Mathematics Probabilities Mathematics Probability Theory and Stochastic Processes


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