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arXiv · 2212.09091

A convergent numerical algorithm for the stochastic growth-fragmentation problem

Dawei Wu·Zhennan Zhou
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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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Dawei Wu, Zhennan Zhou. 2022-12-18. A convergent numerical algorithm for the stochastic growth-fragmentation problem. https://doi.org/10.4208/aam.oa-2023-0035

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