# The deviation matrix of a continuous-time Markov chain

P. Coolen-Schrijner, E.A. van Doorn

Research output: Book/ReportReportOther research output

## 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.
Original language English Enschede University of Twente, Department of Applied Mathematics 20 Published - 2001

### Publication series

Name Memorandum / Department of Applied Mathematics Department of Applied Mathematics, University of Twente 1567 0169-2690

• EWI-3387
• MSC-60J10
• IR-65754
• MSC-60J35
• MSC-60J80
• MSC-60J27