A one-year course in probability theory and the theory of random processes, taught at Princeton University to undergraduate and graduate students, forms the core of the content of this book. It provides a comprehensive, self-contained exposition of classical probability theory and the theory of random processes, and dwells a number of modern topics not addressed in most text-books.

The book offers a detailed discussion of Lebesgue integration, Markov chains, random walks, laws of large numbers, limit theorems, and their relation to Renormalization Group theory. It includes the theory of stationary random processes, martingales, generalized random processes, Brownian motion, stochastic integrals, and stochastic differential equations. One section is devoted to the theory of Gibbs random fields.

This material is essential to many undergraduate and graduate courses. The book can also serve as a reference for scientists using modern probability theory in their research. Its author, Ya. G. Sinai, is one of the world's leading probabilists and mathematical physicists. He has been a professor at Princeton University since 1993 and was awarded the Wolf Prize in Mathemat