Solvability of Langevin differential inclusions with set-valued diffusion terms on Riemannian manifolds |
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Authors: | Svetlana V. Azarina Andrei V. Obukhovskiĭ |
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Affiliation: | Mathematics Faculty , Voronezh State University , Universitetskaya pl. 1, 394006 Voronezh, Russia |
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Abstract: | The existence of weak solution is proved for a Langevin type second-order stochastic differential inclusion on a complete Riemannian manifold, having both drift and diffusion terms set-valued. The construction of solution involves integral operators with Riemannian parallel translation and a special sequence of continuous ?-approximations for an upper semicontinuous set-valued mapping with convex bounded closed values, that is proved to converge point-wise to a Borel measurable selection. |
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Keywords: | Stochastic differential inclusions Langevin equation Riemannian manifolds ?-approximations |
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