Probability-1 / by Albert N. Shiryaev.

Format:

Book

Author/Creator:

Shiryaev, Albert N., Author.

Series:

Graduate Texts in Mathematics, 0072-5285 ; 95

Language:

English

Subjects (All):

Probabilities.

Probability Theory and Stochastic Processes.

Local Subjects:

Probability Theory and Stochastic Processes.

Physical Description:

1 online resource (XVII, 486 p. 39 illus.)

Edition:

3rd ed. 2016.

Place of Publication:

New York, NY : Springer New York : Imprint: Springer, 2016.

Summary:

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.

Contents:

Introduction

Elementary Probability Theory

Mathematical Foundations of Probability Theory

Convergence of Probability Measures. Central Limit Theorem.

Notes:

Includes bibliographical references (pages [465]-469) and indexes.

Description based on publisher supplied metadata and other sources.

ISBN:

0-387-72206-8

OCLC:

1066186232