Transient Solutions of Markov Processes by Krylov Subspaces

In this note we exploit the knowledge embodied in infinitesimal generators of Markov processes to compute efficiently and economically the transient solution of continuous time Markov processes. We consider the Krylov subspace approximation method which has been analysed by Gallopoulos and Saad for solving partial differential equations and linear ordinary differential equations [7, 17]. We place special emphasis on error bounds and stepsize control. We illustrate the usefulness of the approach by providing some application examples.