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.

翻译：随机增长分化模型描述了结构细胞群通过离散时间和连续状态的马尔科夫链条在时间上的演变情况。 模拟这种随机过程及其不变化的计量是值得注意的。 在本文中,我们提出了一个模拟过程和计算不变化计量的数值方案,并表明在适当的假设下,数字链与连续增长分化链相融合,但有明显的误差。 在三角不平等的争论中,我们还能够从数量上估计这两个马尔科夫链条的不变化计量之间的距离。