A convergent numerical algorithm for the stochastic growth-fragmentation problem
Numerical Analysis
2025-05-20 v1 Numerical Analysis
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.
Cite
@article{arxiv.2212.09091,
title = {A convergent numerical algorithm for the stochastic growth-fragmentation problem},
author = {Dawei Wu and Zhennan Zhou},
journal= {arXiv preprint arXiv:2212.09091},
year = {2025}
}