Strong stationary duality for Möbius monotone Markov chains

For Markov chains with a finite, partially ordered state space, we show strong stationary duality under the condition of Möbius monotonicity of the chain. We give examples of dual chains in this context which have no downwards transitions. We illustrate general theory by an analysis of nonsymmetric...

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Bibliographic Details
Published in:Queueing systems 2012-06, Vol.71 (1-2), p.79-95
Main Authors: Lorek, Paweł, Szekli, Ryszard
Format: Article
Language:English
Subjects:
Business and Management
Computer Communication Networks
Control
Eigenvalues
Markov analysis
Operations Research/Decision Theory
Probability Theory and Stochastic Processes
Queuing
Random variables
Studies
Supply Chain Management
Systems Theory
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Summary:For Markov chains with a finite, partially ordered state space, we show strong stationary duality under the condition of Möbius monotonicity of the chain. We give examples of dual chains in this context which have no downwards transitions. We illustrate general theory by an analysis of nonsymmetric random walks on the cube with an interpretation for unreliable networks of queues.
ISSN:0257-0130
1572-9443
DOI:10.1007/s11134-012-9284-z