Flots et series de Taylor stochastiques

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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.

Original languageFrench
Pages (from-to)29-77
Number of pages49
JournalProbability Theory and Related Fields
Issue number1
StatePublished - Feb 1989

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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