Stochastic Modelling and Applied Probability

Numerical Solution of Stochastic Differential Equations

Authors: Kloeden, Peter E., Platen, Eckhard

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About this book

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.

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

Table of contents (17 chapters)

  • Probability and Statistics

    Kloeden, Peter E. (et al.)

    Pages 1-50

  • Probability Theory and Stochastic Processes

    Kloeden, Peter E. (et al.)

    Pages 51-74

  • Ito Stochastic Calculus

    Kloeden, Peter E. (et al.)

    Pages 75-102

  • Stochastic Differential Equations

    Kloeden, Peter E. (et al.)

    Pages 103-160

  • Stochastic Taylor Expansions

    Kloeden, Peter E. (et al.)

    Pages 161-226

Buy this book

eBook $79.99
price for USA (gross)
  • ISBN 978-3-662-12616-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-3-540-54062-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.00
price for USA
  • ISBN 978-3-642-08107-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Numerical Solution of Stochastic Differential Equations
Authors
Series Title
Stochastic Modelling and Applied Probability
Series Volume
23
Copyright
1992
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-12616-5
DOI
10.1007/978-3-662-12616-5
Hardcover ISBN
978-3-540-54062-5
Softcover ISBN
978-3-642-08107-1
Series ISSN
0172-4568
Edition Number
1
Number of Pages
XXXVI, 636
Topics