THE DEVIATION MATRIX OF A CONTINUOUS-TIME MARKOV CHAIN

Authors:
Pauline Coolen-Schrijner;Erik A. Van Doorn
Affiliations:
Department of Mathematical Sciences, University of Durham, Durham, UK, E-mail: pauline.schrijner@durham.ac.uk;Faculty of Mathematical Sciences, University of Twente, Enschede, The Netherlands, E-mail: doorn@math.utwente.nl
Venue:
Probability in the Engineering and Informational Sciences
Year:
2002

Citing 5
Cited 6

Average, sensitive and Blackwell optimal policies in denumerable Markov decisionchains with unbounded rewards

Mathematics of Operations Research
Generalized inverses in discrete time Markov decision process

SIAM Journal on Matrix Analysis and Applications
Asymptotic formulas for Markov processes with applications to simulation

Operations Research
Overcoming Instability In Computing The Fundamental Matrix For A Markov Chain

SIAM Journal on Matrix Analysis and Applications
ON DEVIATION MATRICES FOR BIRTH–DEATH PROCESSES

Probability in the Engineering and Informational Sciences

Predicting queueing delays for multiclass call centers

valuetools '06 Proceedings of the 1st international conference on Performance evaluation methodolgies and tools
Series Expansions For Finite-State Markov Chains

Probability in the Engineering and Informational Sciences
Series Expansions for Continuous-Time Markov Processes

Operations Research
An Approximation Approach for the Deviation Matrix of Continuous-Time Markov Processes with Application to Markov Decision Theory

Operations Research
Poisson's equation for discrete-time quasi-birth-and-death processes

Performance Evaluation
Markov-modulated infinite-server queues with general service times

Queueing Systems: Theory and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

The deviation matrix of an ergodic, continuous-time Markov chain with transition probability matrix P(·) and ergodic matrix &Pgr; is the matrix D ≡ ∫0∞(P(t) − &Pgr;) 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.