A Convergent Numerical Algorithm for the Stochastic Growth-Fragmentation Problem

A Convergent Numerical Algorithm for the Stochastic Growth-Fragmentation Problem

Year:    2024

Author:    Dawei Wu, Zhennan Zhou

Annals of Applied Mathematics, Vol. 40 (2024), Iss. 1 : pp. 71–104

Abstract

The stochastic growth-fragmentation model describes the temporal evolution of a structured cell population through a discrete-time and continuous-state Markov chain. The simulations of this stochastic process and its invariant measure are of interest. In this paper, we propose a numerical scheme for both the simulation of the process and the computation of the invariant measure, and show that under appropriate assumptions, the numerical chain converges to the continuous growth-fragmentation chain with an explicit error bound. With a triangle inequality argument, we are also able to quantitatively estimate the distance between the invariant measures of these two Markov chains.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aam.OA-2023-0035

Annals of Applied Mathematics, Vol. 40 (2024), Iss. 1 : pp. 71–104

Published online:    2024-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    34

Keywords:    Growth-fragmentation model Markov chain numerical approximation space discretization convergence rate.

Author Details

Dawei Wu

Zhennan Zhou