Abstract

It is well known that the numerical stability of many finite difference time-stepping algorithms for solving the Kolmogorov differential equations for Markov jump processes depends on the magnitude of the spectral radius of the rate matrix. In this paper, we develop bounds on the spectral radius that rigorously establish that the spectral radius typically scales in proportion to the maximal jump rate. Our analysis also provides rigorous bounds on the stiffness of the rate matrix, when the process is reversible.

中文翻译：

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关于马尔可夫跳跃过程速率矩阵的谱半径和刚度

抽象的

众所周知，用于解决马尔可夫跳过程的Kolmogorov微分方程的许多有限差分时步算法的数值稳定性取决于速率矩阵的频谱半径的大小。在本文中，我们在光谱半径上建立了边界，严格地确定了光谱半径通常与最大跳跃率成比例地缩放。当过程是可逆的时，我们的分析还为速率矩阵的刚度提供了严格的界限。