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Applicable Analysis
An International Journal
Volume 86, 2007 - Issue 9
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Original Articles

Solvability of Langevin differential inclusions with set-valued diffusion terms on Riemannian manifolds

, &
Pages 1105-1116 | Received 19 Mar 2007, Accepted 04 Jul 2007, Published online: 04 Oct 2007
 

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 ϵ-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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