Volume 40, Issue 1
A Convergent Numerical Algorithm for the Stochastic Growth-Fragmentation Problem

Dawei Wu & Zhennan Zhou

Ann. Appl. Math., 40 (2024), pp. 71-104.

Published online: 2024-02

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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.

  • AMS Subject Headings

37A50, 60J22, 65C40, 37N25

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COPYRIGHT: © Global Science Press

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@Article{AAM-40-71, author = {Wu , Dawei and Zhou , Zhennan}, title = {A Convergent Numerical Algorithm for the Stochastic Growth-Fragmentation Problem}, journal = {Annals of Applied Mathematics}, year = {2024}, volume = {40}, number = {1}, pages = {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.

}, issn = {}, doi = {https://doi.org/10.4208/aam.OA-2023-0035}, url = {http://global-sci.org/intro/article_detail/aam/22928.html} }
TY - JOUR T1 - A Convergent Numerical Algorithm for the Stochastic Growth-Fragmentation Problem AU - Wu , Dawei AU - Zhou , Zhennan JO - Annals of Applied Mathematics VL - 1 SP - 71 EP - 104 PY - 2024 DA - 2024/02 SN - 40 DO - http://doi.org/10.4208/aam.OA-2023-0035 UR - https://global-sci.org/intro/article_detail/aam/22928.html KW - Growth-fragmentation model, Markov chain, numerical approximation, space discretization, convergence rate. AB -

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.

Wu , Dawei and Zhou , Zhennan. (2024). A Convergent Numerical Algorithm for the Stochastic Growth-Fragmentation Problem. Annals of Applied Mathematics. 40 (1). 71-104. doi:10.4208/aam.OA-2023-0035
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