Correcting for Non-Markovian Asymptotic Effects using Markovian Representation

Abstract

Asymptotic properties of Markov Processes, such as steady state probabilities or hazard rate for absorbing states can be efficiently calculated by means of linear algebra even for large-scale problems. This paper discusses the methods for adjusting parameters of the Markov models to account for non-constant transition rates. In particular, transitions with fixed delays are considered along with the transitions that follow Weibull and lognormal distributions. Procedures for both steady-state solutions in the absence of an absorbing state, and for hazard rates to an absorbing state are provided and demonstrated on several examples.