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From Elementary Probability to Stochastic Differential Equations with MAPLE®

  • Sasha Cyganowski
  • Peter Kloeden
  • Jerzy Ombach

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

  • Sasha Cyganowski
    • 1
  • Peter Kloeden
    • 2
  • Jerzy Ombach
    • 3
  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

  • DOI https://doi.org/10.1007/978-3-642-56144-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-42666-0
  • Online ISBN 978-3-642-56144-3
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site
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