Abstract.
In this paper, we study stochastic functional differential equations (sfde's) whose solutions are constrained to live on a smooth compact Riemannian manifold. We prove the existence and uniqueness of solutions to such sfde's. We consider examples of geometrical sfde's and establish the smooth dependence of the solution on finite-dimensional parameters.
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Received: 6 July 1999 / Revised version: 19 April 2000 /¶Published online: 14 June 2001
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Léandre, R., Mohammed, SE. Stochastic functional differential equations on manifolds. Probab Theory Relat Fields 121, 117–135 (2001). https://doi.org/10.1007/PL00008795
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DOI: https://doi.org/10.1007/PL00008795
- Mathematics Subject Classification (2000): Primary 60H10, 60H20; Secondary 60H25
- Key words or phrases: Stochastic functional differential equation – Delay equation, Riemannian manifold – Stochastic parallel transport – Chen-Souriau calculus