The problems and exercises in this book vary in nature and degree of difficulty. Some problems are meant to test the reader's basic understanding, others are of medium-to-high degrees of difficulty and require more creative thinking.

For the first two editions of Probability (GTM 95), each chapter included a comprehensive and diverse set of relevant exercises. While the work on the third edition was still in progress, it was decided that it would be more appropriate to publish a separate book that would comprise all of the exercises from previous editions, in addition to many new exercises. Most of the material in this book consists of exercises created by Shiryaev, collected and compiled over the course of many years while working on many interesting topics. Many of the exercises included in the book contain helpful hints and other relevant information. An appendix at the end of the book contains a summary of the main results, notation and terminology from probability theory that are used throughout the present book, as well as additional material from combinatorics, potential theory and markov chains.

Provides more than 1500 exercises and problems for professors using GTM 95 as a course text Volume is self-contained, although it can be used along with GTM 95 Covers traditional areas of probability theory, as well as recent developments Author is an experienced writer and a well-known expert in the field

Autorentext

Albert Shiryaev is an eminent mathematician who has written several texts on probability and stochastic calculus, which have been translated into several languages. He is the recipient of several honors and awards, including the Humboldt Research Award, Markov prize, and Kolmogorov prize.

Inhalt

Preface.- 1. Elementary Probability Theory.- 2. Mathematical Foundations of Probability Theory.- 3. Convergence of Probability Measures.- 4. Independent Random Variables.- 5. Stationary Random Sequences in Strict Sense.- 6. Stationary Random Sequences in Broad Sense.- 7. Martingales.- 8. Markov Chains.- Appendix.- References.