@book{be8a0a6c2683439d8e92ddfc1cb0f554,

title = "The deviation matrix of a continuous-time Markov chain",

abstract = "The 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 = "MSC-60J10, MSC-60J35, MSC-60J80, MSC-60J27",

author = "P. Coolen-Schrijner and {van Doorn}, E.A.",

year = "2001",

language = "English",

series = "Memorandum / Department of Applied Mathematics",

publisher = "University of Twente, Department of Applied Mathematics",

number = "1567",

}