Flots et series de Taylor stochastiques
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- Arous, G.B. Probab. Th. Rel. Fields (1989) 81: 29. doi:10.1007/BF00343737
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 , Sussmann , Yamato , Fliess and Normand-Cyrot , Krener and Lobry  and Kunita  on the representation of solutions of stochastic differential equations.