Strong stationary duality for Möbius monotone Markov chains

Pawel Lorek, Ryszard Szekli

Abstract:

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.