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 - <p style="text-align: justify;">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.</p>