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Equation différentielle anticipative sur une variété et approximations

Author

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  • Grorud, Axel
  • Pontier, Monique

Abstract

This paper is the sequel of a paper by the authors (1993) and it has a complete version in (1995). We develop a stochastic calculus which allows to integrate non-adapted processes taking their values in the space of second-order 1-forms that are above a manifold valued anticipating process. Using that integration, we study the existence and uniqueness of solution of an anticipating stochastic differential equation in a manifold. This stochastic calculus uses both second-order geometry defined by P.-A. Meyer (1981) and Nualart-Pardoux's duality definition of Skorohod integral (1988).

Suggested Citation

  • Grorud, Axel & Pontier, Monique, 1995. "Equation différentielle anticipative sur une variété et approximations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 38(1), pages 51-61.
  • Handle: RePEc:eee:matcom:v:38:y:1995:i:1:p:51-61
    DOI: 10.1016/0378-4754(93)E0066-E
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