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Flots et series de Taylor stochastiques
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  • Published: 01 February 1989

Flots et series de Taylor stochastiques

  • Gérard Ben Arous1 

Probability Theory and Related Fields volume 81, pages 29–77 (1989)Cite this article

Summary

We study the expansion of the solution of a stochastic differential equation as an (infinite) sum of iterated stochastic (Stratonovitch) integrals. This enables us to give a universal and explicit formula for any invariant diffusion on a Lie group in terms of Lie brackets, as well as a universal and explicit formula for the brownian motion on a Riemannian manifold in terms of derivatives of the curvature tensor. The first of these formulae contains, and extends to the non nilpotent case, the results of Doss [6], Sussmann [17], Yamato [18], Fliess and Normand-Cyrot [7], Krener and Lobry [19] and Kunita [11] on the representation of solutions of stochastic differential equations.

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Authors and Affiliations

  1. Centre de Mathématiques appliquées, Ecole Normale Supérieure, 45 rue d'Ulm, F-75230, Paris Cedex 05, France

    Gérard Ben Arous

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  1. Gérard Ben Arous
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Arous, G.B. Flots et series de Taylor stochastiques. Probab. Th. Rel. Fields 81, 29–77 (1989). https://doi.org/10.1007/BF00343737

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  • Received: 10 March 1986

  • Revised: 14 March 1988

  • Published: 01 February 1989

  • Issue Date: February 1989

  • DOI: https://doi.org/10.1007/BF00343737

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