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Numerical Solution of Stochastic Differential Equations pp 75–102Cite as

Ito Stochastic Calculus

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

Abstract

This chapter provides an introduction to stochastic calculus, in particular to stochastic integration. A fundamental result, the Ito formula, is also derived. This is a stochastic counterpart of the chain rule of deterministic calculus and will be used repeatedly throughout the book. Section 1 summarizes the key concepts and results and should be read by nonspecialists. Mathematical proofs are presented in the subsequent sections.

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Author information

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). Ito Stochastic Calculus. 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_3

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  • DOI: https://doi.org/10.1007/978-3-662-12616-5_3

  • 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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