# Probability-1

## Volume 1

Part of the Graduate Texts in Mathematics book series (GTM, volume 95)

Part of the Graduate Texts in Mathematics book series (GTM, volume 95)

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.

Ergodic theory Markov chain Martingale Probability theory Random variable Random walk Stochastic process Stochastic processes

- DOI https://doi.org/10.1007/978-0-387-72206-1
- Copyright Information Springer Science+Business Media New York 2016
- Publisher Name Springer, New York, NY
- eBook Packages Mathematics and Statistics
- Print ISBN 978-0-387-72205-4
- Online ISBN 978-0-387-72206-1
- Series Print ISSN 0072-5285
- Series Online ISSN 2197-5612
- About this book