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Theory of Probability and Random Processes

  • Leonid Koralov
  • Yakov G. Sinai

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Probability Theory

    1. Front Matter
      Pages 1-1
    2. Leonid Koralov, Yakov G. Sinai
      Pages 3-23
    3. Leonid Koralov, Yakov G. Sinai
      Pages 25-36
    4. Leonid Koralov, Yakov G. Sinai
      Pages 37-57
    5. Leonid Koralov, Yakov G. Sinai
      Pages 59-65
    6. Leonid Koralov, Yakov G. Sinai
      Pages 67-84
    7. Leonid Koralov, Yakov G. Sinai
      Pages 85-99
    8. Leonid Koralov, Yakov G. Sinai
      Pages 101-107
    9. Leonid Koralov, Yakov G. Sinai
      Pages 109-117
    10. Leonid Koralov, Yakov G. Sinai
      Pages 119-130
    11. Leonid Koralov, Yakov G. Sinai
      Pages 131-153
    12. Leonid Koralov, Yakov G. Sinai
      Pages 155-167
  3. Random Processes

    1. Front Matter
      Pages 169-169
    2. Leonid Koralov, Yakov G. Sinai
      Pages 171-179
    3. Leonid Koralov, Yakov G. Sinai
      Pages 181-200
    4. Leonid Koralov, Yakov G. Sinai
      Pages 201-208
    5. Leonid Koralov, Yakov G. Sinai
      Pages 209-229
    6. Leonid Koralov, Yakov G. Sinai
      Pages 231-243
    7. Leonid Koralov, Yakov G. Sinai
      Pages 245-251
    8. Leonid Koralov, Yakov G. Sinai
      Pages 253-272
    9. Leonid Koralov, Yakov G. Sinai
      Pages 273-287
    10. Leonid Koralov, Yakov G. Sinai
      Pages 289-309
    11. Leonid Koralov, Yakov G. Sinai
      Pages 311-339
    12. Leonid Koralov, Yakov G. Sinai
      Pages 341-346
  4. Back Matter
    Pages 347-351

About this book

Introduction

A one-year course in probability theory and the theory of random processes, taught at Princeton University to undergraduate and graduate students, forms the core of the content of this book

It is structured in two parts: the first part providing a detailed discussion of Lebesgue integration, Markov chains, random walks, laws of large numbers, limit theorems, and their relation to Renormalization Group theory. The second part includes the theory of stationary random processes, martingales, generalized random processes, Brownian motion, stochastic integrals, and stochastic differential equations. One section is devoted to the theory of Gibbs random fields.

This material is essential to many undergraduate and graduate courses. The book can also serve as a reference for scientists using modern probability theory in their research.

Keywords

Brownian motion Markov chain Markov process Martingale Probability Probability theory Random variable random processes random walk

Authors and affiliations

  • Leonid Koralov
    • 1
  • Yakov G. Sinai
    • 2
  1. 1.Department of MathematicsUniversity of MarylandCollege ParkUSA
  2. 2.Department of MathematicsPrinceton UniversityNew JerseyUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-68829-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 2007
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-25484-3
  • Online ISBN 978-3-540-68829-7
  • Series Print ISSN 0172-5939
  • Buy this book on publisher's site