Generalized Fokker-Planck equation for piecewise-diffusion processes with boundary hitting resets

Abstract : This paper is concerned with the generalized Fokker-Planck equation for a class of stochastic hybrid processes, where diffusion and instantaneous jumps at the boundary are allowed. The state of the process after a jump is defined by a deterministic reset map. We establish a partial differential equation for the probability density function, which is a generalisation of the usual Fokker-Planck equation for diffusion processes. The result involves a non-local boundary condition, which accounts for the jumping behaviour of the process, and an absorbing boundary condition on the non-characteristic part of the boundary. Two applications are given, with numerical results obtained by finite volume discretization.
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Submitted on : Monday, January 2, 2006 - 12:05:55 PM
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Julien Bect, Hana Baili, Gilles Fleury. Generalized Fokker-Planck equation for piecewise-diffusion processes with boundary hitting resets. MTNS 2006, Jul 2006, Kyoto, Japan. pp.1360-1367. ⟨hal-00016373⟩

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