Principles of Random Walk.

This book is devoted to the study of random walk on the lattice points of ordinary Euclidean space. The theory of random walks, a central part of the theory of Markov chains, is connected with methods from harmonic analysis on the one hand and from potential theory on the other. Prerequisites for the book are some knowledge of two or three of the following areas: probability theory, real variables and measure, analytic functions, Fourier analysis, differential, and integral operators. More than 100 pages of examples and problems illustrate and clarify the presentation. "... 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