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 (with respect to time reversibility) part of the drift. In the case where the diffusion has a limiting velocity we define the asymptotic flux across subsets of the sphere of radius R, when R tends to infinity, and compute its expectation in terms of v.
Asymptotic flux across hypersurfaces for diffusion processes / A. Posilicano, S. Ugolini - In: Proceedings of the International Conference on Stochastic Analysis and Applications / [a cura di] S. Albeverio, A. Boutet de Monvel, H. Ouerdiane. - Dordrecht : Kluwer Academic Publishing, 2004. - ISBN 978-1-4020-2467-2. - pp. 185-197 (( convegno International Conference on Stochastic Analysis and Applications tenutosi a Hammamet, Tunisia nel 2001.
Asymptotic flux across hypersurfaces for diffusion processes
S. UgoliniUltimo
2004
Abstract
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 (with respect to time reversibility) part of the drift. In the case where the diffusion has a limiting velocity we define the asymptotic flux across subsets of the sphere of radius R, when R tends to infinity, and compute its expectation in terms of v.
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