Bect, Julien (École Supérieure d'Électricité (Supélec)), baili, hana (École Supérieure d'Électricité (Supélec)), Fleury, Gilles (École Supérieure d'Électricité (Supélec))

Generalized Fokker-Planck Equation for Piecewise-Diffusion Processes with Boundary Hitting Resets

Scheduled for presentation during the Regular Session "Hybrid Systems I" (WeA05), Wednesday, July 26, 2006, 12:30−12:55, Room F

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on April 19, 2024

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.