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From Elementary Probability to Stochastic Differential Equations with MAPLE®

  • Textbook
  • © 2002

Overview

Authors:
  1. Sasha Cyganowski

    1. Tipperary Institute, Clonmel Co. Tipperary, Ireland

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  2. Peter Kloeden

    1. Fachbereich Mathematik, Johann Wolfgang Goethe Universität Frankfurt am Main, Frankfurt am Main, Germany

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    You can also search for this author in PubMed   Google Scholar

  3. Jerzy Ombach

    1. Institute of Mathematics, Jagiellonian University, ul. Reymonta 4, Krakow, Poland

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  • An elementary introduction to stochastic calculus with the additional benefit of using the symbolic computation programme MAPLE
  • Includes supplementary material: sn.pub/extras

Part of the book series: Universitext (UTX)

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-XVI
    Download chapter PDF

  2. Probability Basics

    • Sasha Cyganowski, Peter Kloeden, Jerzy Ombach
    Pages 1-31

  3. Measure and Integral

    • Sasha Cyganowski, Peter Kloeden, Jerzy Ombach
    Pages 33-60

  4. Random Variables and Distributions

    • Sasha Cyganowski, Peter Kloeden, Jerzy Ombach
    Pages 61-84

  5. Parameters of Probability Distributions

    • Sasha Cyganowski, Peter Kloeden, Jerzy Ombach
    Pages 85-119

  6. A Tour of Important Distributions

    • Sasha Cyganowski, Peter Kloeden, Jerzy Ombach
    Pages 121-159

  7. Numerical Simulations and Statistical Inference

    • Sasha Cyganowski, Peter Kloeden, Jerzy Ombach
    Pages 161-191

  8. Stochastic Processes

    • Sasha Cyganowski, Peter Kloeden, Jerzy Ombach
    Pages 193-227

  9. Stochastic Calculus

    • Sasha Cyganowski, Peter Kloeden, Jerzy Ombach
    Pages 229-247

  10. Stochastic Differential Equations

    • Sasha Cyganowski, Peter Kloeden, Jerzy Ombach
    Pages 249-276

  11. Numerical Methods for SDEs

    • Sasha Cyganowski, Peter Kloeden, Jerzy Ombach
    Pages 277-302

  12. Back Matter

    Pages 303-313
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Keywords

About this book

Measure and integration wereonceconsidered,especially by many ofthe more practically inclined, to be an esoteric area ofabstract mathematics best left to pure mathematicians. However,it has become increasingly obvious in recent years that this area is now an indispensable, even unavoidable, language and provides a fundamental methodology for modern probability theory, stochas­ tic analysis and their applications, especially in financial mathematics. Our aim in writing this book is to provide a smooth and fast introduction to the language and basic results ofmodern probability theory and stochastic differential equations with help ofthe computer manipulator software package MAPLE. It is intended for advanced undergraduate students or graduates, not necessarily in mathematics, to provide an overviewand intuitive background for more advanced studies as wellas somepractical skillsin the use of MAPLE software in the context of probability and its applications. This book is not a conventional mathematics book. Like such books it provides precise definitions and mathematical statements, particularly those based on measure and integration theory, but instead ofmathematical proofs it uses numerous MAPLE experiments and examples to help the reader un­ derstand intuitively the ideas under discussion. The pace increases from ex­ tensive and detailed explanations in the first chapters to a more advanced presentation in the latter part of the book. The MAPLE is handled in a sim­ ilar way, at first with simple commands, then some simple procedures are gardually developed and, finally, the stochastic package is introduced.

Reviews

"... The authors have done a good job. The material is didactically well presented, and motivations are given before definitions are stated. MAPLE, a computer algebra system, is used to illustrate the mathematics and help readers understand the concepts. ..."

Walter Gander, Journal of the American Statistical Association, March 2003, p. 254-255

"... This book is valuable as supplementary text to introductions into probability theory."

F.Hofbauer, Monatshefte für Mathematik 2003, Vol. 138, Issue 1

"... The aim of the book is to supplement conventional mathematical textbooks on probability and stochastics. The book serves its purpose very well. ..."

Evelyn Buckwar, Zentralblatt für Mathematik 987.60002

"The book is based on measure theory which is introduced as smoothly as possible. It is intended for advanced undergraduate students or graduates, not necessarily in mathematics, providing an overview and intuitive background for more advanced studies as well as some practical skills in the use of MAPLE in the context of probability and applications. Although this book contains definitions and theorems, it differs from conventional mathematics books in its use of MAPLE worksheets instead of formal proofs to enable the reader to gain an intuitive understanding of the ideas under concern. As prerequisites the authors assume a familiarity with basic calculus and linear algebra, as well as with elementary ordinary differential equations and, in the final chapter, simple numerical methods for such ODEs."

L'Enseignment Mathematique, Issue 1-2, Vol. 48, 2002, p. 20

Authors and Affiliations

  • Tipperary Institute, Clonmel Co. Tipperary, Ireland

    Sasha Cyganowski

  • Fachbereich Mathematik, Johann Wolfgang Goethe Universität Frankfurt am Main, Frankfurt am Main, Germany

    Peter Kloeden

  • Institute of Mathematics, Jagiellonian University, ul. Reymonta 4, Krakow, Poland

    Jerzy Ombach

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