Stochastic Functional Differential Equations on Manifolds (Conference on Probability and Geometry)

Authors

Salah-Eldin A. Mohammed, Southern Illinois University CarbondaleFollow

Comments

Conference on Probability and Geometry; Institut Élie Cartan; University Université Henri Poincaré Nancy 1; Nancy, France; September 20-25, 1999

Abstract

We prove an existence theorem for solutions of stochastic functional differential equations under smooth constraints in Euclidean space. The initial states are semimartingales on a compact Riemannian manifold. It is shown that, under suitable regularity hypotheses on the coefficients, and given an initial semimartingale, a sfde on a compact manifold admits a unique solution living on the manifold for all time. We also discuss the Chen-Souriau regularity of the solution of the sfde in the initial process. The results are joint work with Remi Leandre.