A Uniform Law of the Iterated Logarithm for Brownian Motion on Compact Riemannian Manifolds.

M. Blümlinger; M. Drmota; R.F. Tichy

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Stochastic differential inclusions of Langevin type on Riemannian manifolds

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We introduce and investigate a set-valued analogue of classical Langevin equation on a Riemannian manifold that may arise as a description of some physical processes (e.g., the motion of the physical Brownian particle) on non-linear configuration space under discontinuous forces or forces with control. Several existence theorems are proved.