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Stochastic functional differential equations on manifolds
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  • Published: September 2001

Stochastic functional differential equations on manifolds

  • Rémi Léandre1 &
  • Salah-Eldin A. Mohammed2 

Probability Theory and Related Fields volume 121, pages 117–135 (2001)Cite this article

  • 154 Accesses

  • 5 Citations

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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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Authors and Affiliations

  1. Institute Elie Cartan, Université de Nancy I, 54000 Vandoenuvre-les-Nancy, France. e-mail: leandre@iecn.u-nancy.fr, , , , , , FR

    Rémi Léandre

  2. Department of Mathematics Southern Illinois University at Carbondale, Carbondale, IL 62901 USA. e-mail: salah@sfde.math.siu.edu, , , , , , US

    Salah-Eldin A. Mohammed

Authors
  1. Rémi Léandre
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  2. Salah-Eldin A. Mohammed
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Additional information

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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  • Issue Date: September 2001

  • DOI: https://doi.org/10.1007/PL00008795

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  • 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
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