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Quasi sure analysis and Stratonovich anticipative stochastic differential equations
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  • Published: March 1993

Quasi sure analysis and Stratonovich anticipative stochastic differential equations

  • Paul Malliavin1 &
  • David Nualart2 

Probability Theory and Related Fields volume 96, pages 45–55 (1993)Cite this article

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  • 12 Citations

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Summary

Consider a stochastic differential equation on ℝd with smooth and bounded coefficients. We apply the techniques of the quasi-sure analysis to show that this equation can be solved pathwise out of a slim set. Furthermore, we can restrict the equation to the level sets of a nondegenerate and smooth random variable, and this provides a method to construct the solution to an anticipating stochastic differential equation with smooth and nondegenerate initial condition.

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Authors and Affiliations

  1. 10, rue Saint Louis en l'Isle, F-75004, Paris, France

    Paul Malliavin

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

    David Nualart

Authors
  1. Paul Malliavin
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  2. David Nualart
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Cite this article

Malliavin, P., Nualart, D. Quasi sure analysis and Stratonovich anticipative stochastic differential equations. Probab. Th. Rel. Fields 96, 45–55 (1993). https://doi.org/10.1007/BF01195882

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  • Received: 03 February 1992

  • Revised: 21 October 1992

  • Issue Date: March 1993

  • DOI: https://doi.org/10.1007/BF01195882

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Mathematics Subject Classification

  • 60H10
  • 60H07
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