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Stochastic geodesics and forward-backward stochastic differential equations on Lie groups

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  • We describe how to generalize to the stochastic case the notion of geodesic on a Lie group equipped with an invariant metric. As second order equations (in time), stochastic geodesics are characterized in terms of stochastic forward-backward differential systems.
        When the group is the diffeomorphisms group this corresponds to a probabilistic description of the Navier-Stokes equations.
    Mathematics Subject Classification: Primary: 58J65, 70H30; Secondary: 60H10, 49Q20.

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