2005/04/28 by Julien Bect, Bect, Julien, Hana Baili +4
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #58J65 (Secondary) #60H10 (Primary) 60J60 #60J75 #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:58J65 #msc:60H10 #msc:60J60 #msc:60J75
paper · pdf · doi:10.48550/arxiv.math/0504583
19 pages. Submitted to Stochastic Processes and their Applications
arxiv created 2005/04/28 · openalex publication_date 2005/04/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We 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.