2022/12/18 by Wu, Dawei, Zhou, Zhennan
#37A50 #37N25 #60J22 #65C40 #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2212.09091
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.