Basic Stochastic Processes

A Course Through Exercises

  • Zdzisław Brzeźniak
  • Tomasz Zastawniak

Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Table of contents

  1. Front Matter
    Pages i-x
  2. Zdzisław Brzeźniak, Tomasz Zastawniak
    Pages 1-15
  3. Zdzisław Brzeźniak, Tomasz Zastawniak
    Pages 17-43
  4. Zdzisław Brzeźniak, Tomasz Zastawniak
    Pages 45-65
  5. Zdzisław Brzeźniak, Tomasz Zastawniak
    Pages 67-83
  6. Zdzisław Brzeźniak, Tomasz Zastawniak
    Pages 85-137
  7. Zdzisław Brzeźniak, Tomasz Zastawniak
    Pages 139-177
  8. Zdzisław Brzeźniak, Tomasz Zastawniak
    Pages 179-222
  9. Back Matter
    Pages 223-225

About this book


This book has been designed for a final year undergraduate course in stochastic processes. It will also be suitable for mathematics undergraduates and others with interest in probability and stochastic processes, who wish to study on their own. The main prerequisite is probability theory: probability measures, random variables, expectation, independence, conditional probability, and the laws of large numbers. The only other prerequisite is calculus. This covers limits, series, the notion of continuity, differentiation and the Riemann integral. Familiarity with the Lebesgue integral would be a bonus. A certain level of fundamental mathematical experience, such as elementary set theory, is assumed implicitly. Throughout the book the exposition is interlaced with numerous exercises, which form an integral part of the course. Complete solutions are provided at the end of each chapter. Also, each exercise is accompanied by a hint to guide the reader in an informal manner. This feature will be particularly useful for self-study and may be of help in tutorials. It also presents a challenge for the lecturer to involve the students as active participants in the course.


Brownian motion Markov chain Martingale Poisson process Probability theory Random variable Uniform integrability filtration renewal theory stochastic process

Authors and affiliations

  • Zdzisław Brzeźniak
    • 1
  • Tomasz Zastawniak
    • 1
  1. 1.Department of MathematicsUniversity of HullHullUK

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag London Limited 1999
  • Publisher Name Springer, London
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-76175-4
  • Online ISBN 978-1-4471-0533-6
  • Series Print ISSN 1615-2085
  • Buy this book on publisher's site
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