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© 2002

From Elementary Probability to Stochastic Differential Equations with MAPLE®

  • An elementary introduction to stochastic calculus with the additional benefit of using the symbolic computation programme MAPLE

Textbook

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages I-XVI
  2. Sasha Cyganowski, Peter Kloeden, Jerzy Ombach
    Pages 1-31
  3. Sasha Cyganowski, Peter Kloeden, Jerzy Ombach
    Pages 33-60
  4. Sasha Cyganowski, Peter Kloeden, Jerzy Ombach
    Pages 61-84
  5. Sasha Cyganowski, Peter Kloeden, Jerzy Ombach
    Pages 85-119
  6. Sasha Cyganowski, Peter Kloeden, Jerzy Ombach
    Pages 121-159
  7. Sasha Cyganowski, Peter Kloeden, Jerzy Ombach
    Pages 161-191
  8. Sasha Cyganowski, Peter Kloeden, Jerzy Ombach
    Pages 193-227
  9. Sasha Cyganowski, Peter Kloeden, Jerzy Ombach
    Pages 229-247
  10. Sasha Cyganowski, Peter Kloeden, Jerzy Ombach
    Pages 249-276
  11. Sasha Cyganowski, Peter Kloeden, Jerzy Ombach
    Pages 277-302
  12. Back Matter
    Pages 303-313

About this book

Introduction

The authors provide a fast introduction to probabilistic and statistical concepts necessary to understand the basic ideas and methods of stochastic differential equations. 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 its 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 consideration. 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. Although statistics is not systematically treated, they introduce statistical concepts such as sampling, estimators, hypothesis testing, confidence intervals, significance levels and p-values and use them in a large number of examples, problems and simulations.

Keywords

Estimator Maple Measure Probability distribution Random variable Stochastic Differential Equations Stochastic Processes Stochastic calculus linear algebra numerical methods simulation statistics

Authors and affiliations

  1. 1.Tipperary InstituteClonmel Co. TipperaryIreland
  2. 2.Fachbereich MathematikJohann Wolfgang Goethe Universität Frankfurt am MainFrankfurt am MainGermany
  3. 3.Institute of MathematicsJagiellonian Universityul. Reymonta 4KrakowPoland

Bibliographic information

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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