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Analysis and computation of probability density functions for a 1-D impulsively controlled diffusion process. (Analyse et calcul des fonctions de densité de probabilité pour un processus de diffusion en dimension 1 contrôlé par impulsion.) (English) Zbl 1501.60044

Summary: This paper proposes appropriate boundary conditions to be equipped with Kolmogorov’s forward equation that governs a stationary probability density function for a 1-D impulsively controlled diffusion process and derives an exact probability density function. The boundary conditions are verified numerically with a Monte Carlo approach. A finite-volume method for solving the equation is also presented and its accuracy is investigated through numerical experiments.

MSC:

60J60 Diffusion processes
65C05 Monte Carlo methods
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