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Product Expansions of Exponential Lie Series and the Discretization of Stochastic Differential Equations

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Stochastic Differential Systems, Stochastic Control Theory and Applications

Part of the book series: The IMA Volumes in Mathematics and Its Applications ((IMA,volume 10))

Abstract

We show how to rewrite the usual discretization schemes for stochastic differential equations in a way that uses the minimum necessary number of nonredundant iterated integrals. Also, we obtain schemes with the property that, if the true solution evolves in a submanifold, then the same is true of the approximation given by the scheme.

Partially supported by NSF Grant No. DMS83–01678–01 and by the Institute for Mathematics and its Applications, University of Minnesota

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Authors and Affiliations

  1. Mathematics Department, Rutgers University, New Brunswick, N.J., 08903, USA

    H. J. Sussmann

Authors
  1. H. J. Sussmann
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Editor information

Editors and Affiliations

  1. Division of Applied Mathematics, Brown University, 02912, Providence, Rhode Island, USA

    Wendell Fleming

  2. Ceremade, Universite Paris-Dauphine, Place de Lattre de Tassigny, 75775, Paris Cedex 16, France

    Pierre-Louis Lions

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© 1988 Springer-Verlag New York Inc.

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Sussmann, H.J. (1988). Product Expansions of Exponential Lie Series and the Discretization of Stochastic Differential Equations. In: Fleming, W., Lions, PL. (eds) Stochastic Differential Systems, Stochastic Control Theory and Applications. The IMA Volumes in Mathematics and Its Applications, vol 10. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8762-6_32

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  • DOI: https://doi.org/10.1007/978-1-4613-8762-6_32

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-8764-0

  • Online ISBN: 978-1-4613-8762-6

  • eBook Packages: Springer Book Archive

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