On the spectral radius and stiffness of Markov jump process rate matricesPeter W. Glynn and Alex Infanger Stochastic Models (2020). 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. |