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.