# Brownian Motion and Diffusion

Book

1. Front Matter
Pages i-xii
2. David Freedman
Pages 1-101
3. David Freedman
Pages 102-179
4. David Freedman
Pages 180-217
5. Back Matter
Pages 218-231

### Introduction

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 thot:sand 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 - Me, B & D, and ACM. I wrote the first two books for beginning graduate students with some knowledge of probability; if you can follow Sections 3.4 to 3.9 of Brownian Motion and Diffusion 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 spe­ cific disclaimers; 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 argue in a minute, my demonstrations are easier technically. If I wrote them down well enough, you may come to agree.

### Keywords

Brownian motion Brownsche Bewegung Diffusion Diffusionsprozess (Statistik) Markov chain Markov process Martingale Motion Variance law of the iterated logarithm local time

#### Authors and affiliations

1. 1.Department of StatisticsUniversity of CaliforniaBerkeleyUSA

### Bibliographic information

• Book Title Brownian Motion and Diffusion
• Authors David Freedman
• DOI https://doi.org/10.1007/978-1-4615-6574-1
• Copyright Information Springer-Verlag New York 1983
• Publisher Name Springer, New York, NY
• eBook Packages
• Hardcover ISBN 978-0-387-90805-2
• Softcover ISBN 978-1-4615-6576-5
• eBook ISBN 978-1-4615-6574-1
• Edition Number 1
• Number of Pages XII, 231
• Number of Illustrations 0 b/w illustrations, 0 illustrations in colour