Fokker-Planck-Kolmogorov equation for stochastic differential equations with boundary hitting resets

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dc.creatorBect, Julien
dc.creatorBaili, Hana
dc.creatorFleury, Gilles
dc.date2005-04-28
dc.date.accessioned2026-07-07T05:19:30Z
dc.date.available2026-07-07T05:19:30Z
dc.descriptionWe consider a Markov process on a Riemannian manifold, which solves a stochastic differential equation in the interior of the manifold and jumps according to a deterministic reset map when it reaches the boundary. We derive a partial differential equation for the probability density function, involving a non-local boundary condition which accounts for the jumping behaviour of the process. This is a generalisation of the usual Fokker-Planck-Kolmogorov equation for diffusion processes. The result is illustrated with an example in the field of stochastic hybrid systems.
dc.description19 pages. Submitted to Stochastic Processes and their Applications
dc.identifierhttps://arxiv.org/abs/math/0504583
dc.identifierhttp://arxiv.org/abs/math/0504583
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75038
dc.subjectProbability
dc.subject60H10 (Primary) 60J60, 60J75, 58J65 (Secondary)
dc.titleFokker-Planck-Kolmogorov equation for stochastic differential equations with boundary hitting resets
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