Asymptotic flux across hypersurfaces for diffusion processes

Details Asymptotic flux across hypersurfaces for diffusion processes Asymptotic flux across hypersurfaces for diffusion processes

2002-12-02

arxiv.org/abs/math/0212020v2

Mathematics

Probability

Revised version. To appear in Proceedings of the International Conference on Stochastic Analysis and Applications, a volume de

Scientific paper

We suggest a rigorous definition of the pathwise flux across the boundary of a bounded open set for transient finite energy diffusion processes. The expectation of such a flux has the property of depending only on the current velocity $v$, the nonsymmetric (as regards time reversibility) part of the drift. In the case the diffusion has a limiting velocity we then define the asymptotic (as $R\uparrow\infty$) flux across subsets of the sphere of radius $R$ and compute its expectation, again in terms of $v$.

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