Probability-1
Volume 1

Authors: Albert N. Shiryaev



Successfully synthesizes the most important classical ideas and results with many of the major achievements of modern probability theory

Author provides clear and comprehensive introduction to probability theory

Third edition now has a chapter on the history of probability theory

Covers in detail topics including ergodic theory, weak convergence of probability measures, stationary stochastic processes, and the Kalman-Bucy filter



This book contains a systematic treatment of probability from the ground up, starting with intuitive ideas and gradually developing more sophisticated subjects, such as random walks, martingales, Markov chains, the measure-theoretic foundations of probability theory, weak convergence of probability measures, and the central limit theorem. Many examples are discussed in detail, and there are a large number of exercises. The book is accessible to advanced undergraduates and can be used as a text for independent study.

To accommodate the greatly expanded material in the third edition of Probability, the book is now divided into two volumes. This first volume contains updated references and substantial revisions of the first three chapters of the second edition. In particular, new material has been added on generating functions, the inclusion-exclusion principle, theorems on monotonic classes (relying on a detailed treatment of “π-λ” systems), and the fundamental theorems of mathematical statistics.