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.
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty