# Problems in Probability

• Albert N. Shiryaev
Textbook

Part of the Problem Books in Mathematics book series (PBM)

1. Front Matter
Pages i-xii
2. Albert N. Shiryaev
Pages 1-58
3. Albert N. Shiryaev
Pages 59-179
4. Albert N. Shiryaev
Pages 181-232
5. Albert N. Shiryaev
Pages 233-257
6. Albert N. Shiryaev
Pages 259-266
7. Albert N. Shiryaev
Pages 267-281
8. Albert N. Shiryaev
Pages 283-327
9. Albert N. Shiryaev
Pages 329-357
10. Back Matter
Pages 359-427

### Introduction

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.

### Keywords

Andrew Lyasoff

#### Authors and affiliations

• Albert N. Shiryaev
• 1
1. 1.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia