Correcting for Non-Markovian Asymptotic Effects using Markovian Representation

05/02/2017

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by   Vitali Volovoi, et al.

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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.