Problems in Probability (Problem Books in Mathematics) - Softcover

Shiryaev, Albert N.

Softcover

ISBN 10: 1489999418 ISBN 13: 9781489999412

Publisher: Springer, 2014

Synopsis

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.

About this title

About the Author

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.

From the Back Cover

Problems in Probability comprises one of the most comprehensive, nearly encyclopedic, collections of problems and exercises in probability theory. Albert Shiryaev has skillfully created, collected, and compiled the exercises in this text over the course of many years while working on topics which interested him the most. A substantial number of the exercises resulted from diverse sources such as textbooks, lecture notes, exercise manuals, monographs, and discussions that took place during special seminars for graduate and undergraduate students. Many problems contain helpful hints and other relevant comments and a portion of the material covers some important applications from optimal control and mathematical finance. Readers of diverse backgrounds―from students to researchers―will find a great deal of value in this book and can treat the work as an exercise manual, a handbook, or as a supplementary text to a course in probability theory, control, and mathematical finance.

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. Other problems are meant to develop additional theoretical concepts and tools or to familiarize the reader with various facts that are not necessarily covered in mainstream texts. Additional problems are related to the passage from random walk to Brownian motions and Brownian bridges. The appendix contains a summary of the main results, notation and terminology that are used throughout the book. It also contains additional material from combinatorics, potential theory and Markov chains―subjects that are not covered in the book, but are nevertheless needed for many of the exercises included here.

Edition details

• Publisher: Springer
• Publication date: 2014
• ISBN 10: 1489999418
• ISBN 13: 9781489999412
• Binding: Paperback
• Language: English
• Number of pages: 440