A Positive and Monotone Numerical Scheme for Volterra-Renewal Equations with Space Fluxes

Authors

  • Mario Annunziato Dipartimento di Matematica, Universit`a degli Studi di Salerno, Via G. Paolo II 132, 84084 Fisciano (SA) Italy
  • Eleonora Messina Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Universit`a degli Studi di Napoli “Federico II”, Via Cintia, Monte S. Angelo, 80126 Napoli, Italy

DOI:

https://doi.org/10.4208/jcm.1708-m2017-0015

Keywords:

Volterra renewal, Piecewise deterministic process, Monotone positive numerical scheme, Bernstein polynomials.

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.

Downloads

Published

2018-08-23

Issue

Vol. 37 No. 1 (2019)

Section

Articles