论文标题
一种随机生长碎片问题的收敛数值算法
A convergent numerical algorithm for the stochastic growth-fragmentation problem
论文作者
论文摘要
随机生长碎片模型通过离散的时间和持续状态马尔可夫链描述了结构化细胞种群的时间演变。这种随机过程及其不变措施的模拟是有意义的。在本文中，我们提出了一个数值方案，以模拟该过程和不变度度量的计算，并表明在适当的假设下，数值链会收敛到具有显式误差绑定的连续生长裂差链。有了三角形的不等式论证，我们还能够定量估计这两个马尔可夫链的不变度量之间的距离。
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.
