Stochastic differential equations driven by loops

Abstract

We study the properties of solutions of stochastic differential equations driven by processes generating loops in free nilpotent groups. We are in particular interested in existence and smoothness for the density.

Some of the results have been announced in the CRAS note, "Equations differentielles stochastiques conduites par des lacets dans les groupes de Carnot." C. R. Math. Acad. Sci. Paris 338 (2004), no. 9, 719-722