@article{2c47b7995a8c4691a443e002cf3e630e,
title = "The deviation matrix of a continuous-time Markov chain",
abstract = "he deviation matrix of an ergodic, continuous-time Markov chain with transition probability matrix $P(.)$ and ergodic matrix $\Pi$ is the matrix $D \equiv \int_0^{\infty} (P(t)-\Pi)dt$. We give conditions for $D$ to exist and discuss properties and a representation of $D$. The deviation matrix of a birth-death process is investigated in detail. We also describe a new application of deviation matrices by showing that a measure for the convergence to stationarity of a stochastically increasing Markov chain can be expressed in terms of the elements of the deviation matrix of the chain.",
keywords = "Birth-death process, Ergodic Markov chain, Deviation matrix, Convergence to stationarity",
author = "Pauline Coolen-Schrijner and {van Doorn}, {Erik A.}",
year = "2002",
doi = "10.1017/S0269964802163066",
language = "English",
volume = "16",
pages = "351--366",
journal = "Probability in the engineering and informational sciences",
issn = "0269-9648",
publisher = "Cambridge University Press",
number = "3",
}