A Convergent Numerical Algorithm for the Stochastic Growth-Fragmentation Problem  

作　　者：Dawei Wu Zhennan Zhou 

机构地区：[1]School of Mathematical Sciences,Peking University,Beijing 100871,China [2]Beijing International Center for Mathematical Research,Peking University,Beijing 100871,China

出　　处：《Annals of Applied Mathematics》2024年第1期71-104,共34页应用数学年刊（英文版）

基　　金：partially supported by the National Key R&D Program of China,Project No.2020YFA0712000;NSFC Grant No.12031013 and 12171013.

摘　　要：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.

关 键 词：Growth-fragmentation model Markov chain numerical approximation space discretization convergence rate 

分 类 号：O211.62[理学—概率论与数理统计]