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Numerical Solution of Stochastic Differential Equations

  • Peter E. Kloeden
  • Eckhard Platen

Part of the Applications of Mathematics book series (SMAP, volume 23)

Table of contents

  1. Front Matter
    Pages I-XXXVI
  2. Preliminaries

    1. Peter E. Kloeden, Eckhard Platen
      Pages 1-50
    2. Peter E. Kloeden, Eckhard Platen
      Pages 51-74
  3. Stochastic Differential Equations

    1. Peter E. Kloeden, Eckhard Platen
      Pages 75-102
    2. Peter E. Kloeden, Eckhard Platen
      Pages 103-160
    3. Peter E. Kloeden, Eckhard Platen
      Pages 161-226
  4. Applications of Stochastic Differential Equations

    1. Peter E. Kloeden, Eckhard Platen
      Pages 227-252
    2. Peter E. Kloeden, Eckhard Platen
      Pages 253-275
  5. Time Discrete Approximations

    1. Peter E. Kloeden, Eckhard Platen
      Pages 277-303
    2. Peter E. Kloeden, Eckhard Platen
      Pages 305-337
  6. Strong Approximations

    1. Peter E. Kloeden, Eckhard Platen
      Pages 339-371
    2. Peter E. Kloeden, Eckhard Platen
      Pages 373-394
    3. Peter E. Kloeden, Eckhard Platen
      Pages 395-425
    4. Peter E. Kloeden, Eckhard Platen
      Pages 427-456
  7. Weak Approximations

    1. Peter E. Kloeden, Eckhard Platen
      Pages 457-484
    2. Peter E. Kloeden, Eckhard Platen
      Pages 485-510
    3. Peter E. Kloeden, Eckhard Platen
      Pages 511-527
    4. Peter E. Kloeden, Eckhard Platen
      Pages 529-548
  8. Back Matter
    Pages 549-636

About this book

Introduction

The numerical analysis of stochastic differential equations differs significantly from that of ordinary differential equations due to peculiarities of stochastic calculus. This book provides an introduction to stochastic calculus and stochastic differential equations, in both theory and applications, emphasising the numerical methods needed to solve such equations. It assumes of the reader an undergraduate background in mathematical methods typical of engineers and physicists, though many chapters begin with a descriptive summary. The book is also accessible to others who only require numerical recipes. The stochastic Taylor expansion provides the basis for the discrete time numerical methods for differential equations. The book presents many new results on high-order methods for strong sample path approximations and for weak functional approximations, including implicit, predictor-corrector, extra-polation and variance-reduction methods. Besides serving as a basic text on such methods, the book offers the reader ready access to a large number of potential research problems in a field that is just beginning to expand rapidly and is widely applicable. To help the reader to develop an intuitive understanding of the underlying mathematics and hand-on numerical skills, exercises and over 100 PC-Exercises are included.

Keywords

Stochastic Processes Stochastic calculus Stochastic differential equations Variance calculus diffusion processes linear optimization modeling numerical analysis numerical methods numerical schemes numerical solution statistics stochastic Taylor expansion time-discrete approximations

Authors and affiliations

  • Peter E. Kloeden
    • 1
  • Eckhard Platen
    • 2
  1. 1.Fachbereich MathematikJohann Wolfgang Goethe-UniversitätFrankfurt am MainGermany
  2. 2.School of Mathematical Sciences and School of Finance & EconomicsUniversity of Technology, SydneyBroadwayAustralia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-12616-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 1992
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-08107-1
  • Online ISBN 978-3-662-12616-5
  • Series Print ISSN 0172-4568
  • Buy this book on publisher's site