Principles of Random Walk (Graduate Texts in Mathematics)

This book is devoted exclusively to a very special class of random processes, namely to random walk on the lattice points of ordinary Euclidean space. The author considered this high degree of specialization worthwhile, because of the theory of such random walks is far more complete than that of any larger class of Markov chains. The book will present no technical difficulties to the readers with some solid experience in analysis in two or three of the following areas: probability theory, real variables and measure, analytic functions, Fourier analysis, differential and integral operators. There are almost 100 pages of examples and problems.

From the reviews: .,."This book certainly covers almost all major topics in the theory of random walk. It will be invaluable to both pure and applied probabilists, as well as to many people in analysis. References for the methods and results involved are very good. A useful interdependence guide is given. Excellent choice is made of examples, which are mostly concerned with very concrete calculations. Each chapter contains complementary material in the form of remarks, examples and problems which are often themselves interesting theorems." (T. Watanabe, Mathematical Reviews) From the reviews of the second edition: "The most valuable new feature of the second edition is a supplementary bibliography covering results obtained from 1964 to 1976, which have been carefully included into the text. The publication of the second printing now encourages the reader to reconstruct the trains of thought of the founders of the theory of random walk. a ] For those knowing already a little bit about the theory this book is an invaluable source of ideas, impressive connections and results." (Markus Reiss, Zentralblatt MATH, Vol. 979, 2002)