Abstract
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 language | French |
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Pages (from-to) | 29-77 |
Number of pages | 49 |
Journal | Probability Theory and Related Fields |
Volume | 81 |
Issue number | 1 |
DOIs | |
State | Published - Feb 1989 |
ASJC Scopus subject areas
- Analysis
- Statistics and Probability
- Statistics, Probability and Uncertainty