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Stochastic calculus with anticipating integrands
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  • Published: August 1988

Stochastic calculus with anticipating integrands

  • D. Nualart1 &
  • E. Pardoux2 

Probability Theory and Related Fields volume 78, pages 535–581 (1988)Cite this article

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Summary

We study the stochastic integral defined by Skorohod in [24] of a possibly anticipating integrand, as a function of its upper limit, and establish an extended Itô formula. We also introduce an extension of Stratonovich's integral, and establish the associated chain rule. In all the results, the adaptedness of the integrand is replaced by a certain smoothness requirement.

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Authors and Affiliations

  1. Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, E-08007, Barcelona, Spain

    D. Nualart

  2. Mathématiques case H, Université de Provence, F-13331, Marseille Cedex 3, France

    E. Pardoux

Authors
  1. D. Nualart
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  2. E. Pardoux
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Nualart, D., Pardoux, E. Stochastic calculus with anticipating integrands. Probab. Th. Rel. Fields 78, 535–581 (1988). https://doi.org/10.1007/BF00353876

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  • Received: 30 October 1986

  • Revised: 28 December 1987

  • Issue Date: August 1988

  • DOI: https://doi.org/10.1007/BF00353876

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Keywords

  • Stochastic Process
  • Probability Theory
  • Statistical Theory
  • Chain Rule
  • Stochastic Calculus
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