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Numerical Solution of Stochastic Differential Equations

  • Book
  • © 1992

Overview

Authors:
  1. Peter E. Kloeden

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

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  2. Eckhard Platen

    1. School of Mathematical Sciences and School of Finance & Economics, University of Technology, Sydney, Broadway, Australia

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    You can also search for this author in PubMed   Google Scholar

  • The book is interdisciplinary in its appoach and orientation
  • It places equal emphasis on both theory and applications
  • Besides serving as a basic text on stochastic differential equations it derives and discusses the numerical methods needed to solve such equations
  • Includes supplementary material: sn.pub/extras

Part of the book series: Stochastic Modelling and Applied Probability (SMAP, volume 23)

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Table of contents (17 chapters)

  1. Front Matter

    Pages I-XXXVI
    Download chapter PDF

  2. Preliminaries

    1. Probability and Statistics

      • Peter E. Kloeden, Eckhard Platen
      Pages 1-50

    2. Probability Theory and Stochastic Processes

      • Peter E. Kloeden, Eckhard Platen
      Pages 51-74

  3. Stochastic Differential Equations

    1. Ito Stochastic Calculus

      • Peter E. Kloeden, Eckhard Platen
      Pages 75-102

    2. Stochastic Differential Equations

      • Peter E. Kloeden, Eckhard Platen
      Pages 103-160

    3. Stochastic Taylor Expansions

      • Peter E. Kloeden, Eckhard Platen
      Pages 161-226

  4. Applications of Stochastic Differential Equations

    1. Modelling with Stochastic Differential Equations

      • Peter E. Kloeden, Eckhard Platen
      Pages 227-252

    2. Applications of Stochastic Differential Equations

      • Peter E. Kloeden, Eckhard Platen
      Pages 253-275

  5. Time Discrete Approximations

    1. Time Discrete Approximation of Deterministic Differential Equations

      • Peter E. Kloeden, Eckhard Platen
      Pages 277-303

    2. Introduction to Stochastic Time Discrete Approximation

      • Peter E. Kloeden, Eckhard Platen
      Pages 305-337

  6. Strong Approximations

    1. Strong Taylor Approximations

      • Peter E. Kloeden, Eckhard Platen
      Pages 339-371

    2. Explicit Strong Approximations

      • Peter E. Kloeden, Eckhard Platen
      Pages 373-394

    3. Implicit Strong Approximations

      • Peter E. Kloeden, Eckhard Platen
      Pages 395-425

    4. Selected Applications of Strong Approximations

      • Peter E. Kloeden, Eckhard Platen
      Pages 427-456

  7. Weak Approximations

    1. Weak Taylor Approximations

      • Peter E. Kloeden, Eckhard Platen
      Pages 457-484

    2. Explicit and Implicit Weak Approximations

      • Peter E. Kloeden, Eckhard Platen
      Pages 485-510

    3. Variance Reduction Methods

      • Peter E. Kloeden, Eckhard Platen
      Pages 511-527

    4. Selected Applications of Weak Approximations

      • Peter E. Kloeden, Eckhard Platen
      Pages 529-548

  8. Back Matter

    Pages 549-636
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Keywords

About this book

The aim of this book is to provide an accessible introduction to stochastic differ­ ential equations and their applications together with a systematic presentation of methods available for their numerical solution. During the past decade there has been an accelerating interest in the de­ velopment of numerical methods for stochastic differential equations (SDEs). This activity has been as strong in the engineering and physical sciences as it has in mathematics, resulting inevitably in some duplication of effort due to an unfamiliarity with the developments in other disciplines. Much of the reported work has been motivated by the need to solve particular types of problems, for which, even more so than in the deterministic context, specific methods are required. The treatment has often been heuristic and ad hoc in character. Nevertheless, there are underlying principles present in many of the papers, an understanding of which will enable one to develop or apply appropriate numerical schemes for particular problems or classes of problems.

Reviews

"... the authors draw upon their own research and experiences in obviously many disciplines... considerable time has obviously been spent writing this in the simplest language possible. This was not an easy task... Their exposition stresses clarity, not formality - a very welcome approach." ZAMP

Authors and Affiliations

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

    Peter E. Kloeden

  • School of Mathematical Sciences and School of Finance & Economics, University of Technology, Sydney, Broadway, Australia

    Eckhard Platen

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