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Numerical Solution of Stochastic Differential Equations pp 161–226Cite as

Stochastic Taylor Expansions

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

Abstract

In this chapter stochastic Taylor expansions are derived and investigated. They generalize the deterministic Taylor formula as well as the Ito formula and allow various kinds of higher order approximations of functionals of diffusion processes to be made. These expansions are the key to the stochastic numerical analysis which we shall develop in the second half of this book. Apart from Section 1, which provides an introductory overview, this chapter could be omitted at the first reading of the book.

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Authors and Affiliations

  1. Fachbereich Mathematik, Johann Wolfgang Goethe-Universität, Postfach 11 19 32, D-60054, Frankfurt am Main, Germany

    Peter E. Kloeden

  2. School of Mathematical Sciences and School of Finance & Economics, University of Technology, Sydney, City Campus Broadway, GPO Box 123, 2007, Broadway, NSW, Australia

    Eckhard Platen

Authors
  1. Peter E. Kloeden
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  2. Eckhard Platen
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© 1992 Springer-Verlag Berlin Heidelberg

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Kloeden, P.E., Platen, E. (1992). Stochastic Taylor Expansions. In: Numerical Solution of Stochastic Differential Equations. Applications of Mathematics, vol 23. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-12616-5_5

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  • DOI: https://doi.org/10.1007/978-3-662-12616-5_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-08107-1

  • Online ISBN: 978-3-662-12616-5

  • eBook Packages: Springer Book Archive

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