Finite volume computation for the non-stationary probability density function of an impulsively controlled 1-D diffusion process

Abstract

We derive a Fokker Planck Equation (FPE) governing probability density functions (PDFs) of an impulsively controlled 1-D diffusion process in seasonal population management problems. Two interventions are considered: perfect (completely controllable) and imperfect interventions (not completely controllable). The FPE is an initial-and boundary-value problem subject to a non-local boundary condition along a moving boundary. We show that an finite volume method (FVM) with a domain transformation realizes a conservative discretization for the FPE. We demonstrate that the computed PDFs with the FVM and those with a Monte Carlo method agree well.