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Basic Stochastic Processes

A Course Through Exercises

  • Textbook
  • © 1999

Overview

Authors:
  1. Zdzisław Brzeźniak

    1. Department of Mathematics, University of Hull, Hull, UK

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    You can also search for this author in PubMed   Google Scholar

  2. Tomasz Zastawniak

    1. Department of Mathematics, University of Hull, Hull, UK

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Informal hints and fully worked solutions accompanying the exercises
  • Strong emphasis on self-study
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Review of Probability

    • Zdzisław Brzeźniak, Tomasz Zastawniak
    Pages 1-15

  3. Conditional Expectation

    • Zdzisław Brzeźniak, Tomasz Zastawniak
    Pages 17-43

  4. Martingales in Discrete Time

    • Zdzisław Brzeźniak, Tomasz Zastawniak
    Pages 45-65

  5. Martingale Inequalities and Convergence

    • Zdzisław Brzeźniak, Tomasz Zastawniak
    Pages 67-83

  6. Markov Chains

    • Zdzisław Brzeźniak, Tomasz Zastawniak
    Pages 85-137

  7. Stochastic Processes in Continuous Time

    • Zdzisław Brzeźniak, Tomasz Zastawniak
    Pages 139-177

  8. Itô Stochastic Calculus

    • Zdzisław Brzeźniak, Tomasz Zastawniak
    Pages 179-222

  9. Back Matter

    Pages 223-225
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Keywords

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 willbe 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.

Reviews

This book fulfils its aim of providing good and interesting material for advanced undergraduate study.

The Times Higher Education Supplement

This is probably one of the best books to begin learning about the sometimes complex topic of stochastic calculus and stochastic processes from a more mathematical approach. Some literature are often accused of unnecessarily complicating the subject when applied to areas of finance. With this book you are allowed to explore the rigorous side of stochastic calculus, yet maintain a physical insight of what is going on. The authors have concentrated on the most important and useful topics that are encountered in common physical and financial systems

www.quantnotes.com

 

Authors and Affiliations

  • Department of Mathematics, University of Hull, Hull, UK

    Zdzisław Brzeźniak, Tomasz Zastawniak

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