Year: 2019
Author: Mario Annunziato, Eleonora Messina
Journal of Computational Mathematics, Vol. 37 (2019), Iss. 1 : pp. 33–47
Abstract
We study a numerical method for solving a system of Volterra-renewal integral equations with space fluxes, that represents the Chapman-Kolmogorov equation for a class of piecewise deterministic stochastic processes. The solution of this equation is related to the time dependent distribution function of the stochastic process and it is a non-negative and non-decreasing function of the space. Based on the Bernstein polynomials, we build up and prove a non-negative and non-decreasing numerical method to solve that equation, with quadratic convergence order in space.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1708-m2017-0015
Journal of Computational Mathematics, Vol. 37 (2019), Iss. 1 : pp. 33–47
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Volterra renewal Piecewise deterministic process Monotone positive numerical scheme Bernstein polynomials.