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Mathematics - Probability Theory and Stochastic Processes | Problems in Probability

Problems in Probability

Shiryaev, Albert N.

Translated by Lyasoff, A.

Original russian edition published by MCCME, Moscow

2012, XII, 428 p. With Original Russian Edition of "Probability": Shir\t{ia}ev, Al’bert Nikolaevich, Zadachi po Teorii Vero\t{ia}tnoste\u{i}, Moscow: MCCME, ©2006..

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  • 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

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.

Content Level » Graduate

Keywords » Andrew Lyasoff

Related subjects » Probability Theory and Stochastic Processes

Table of contents 

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.

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