Duality and Intertwining for discrete Markov kernels: relations and examples

Thierry Huillet (1) , Servet Martinez (2)

1 LPTM - UMR 8089 - Laboratoire de Physique Théorique et Modélisation
2 Departamento de Ingenieria Matematica, Centro Modelamiento Matematico

We work out some relations between duality and intertwining in the context of discrete Markov chains, fixing up the background of previous relations first established for birth and death chains and their Siegmund duals. In view of the results, the monotone properties resulting from the Siegmund dual of birth and death chains are revisited in some detail, with emphasis on the non neutral Moran model. We also introduce an ultrametric type dual extending the Siegmund kernel. Finally we discuss the sharp dual, following closely the Diaconis-Fill study.

Mots clés: sharp dual.; Duality; Intertwining; Siegmund dual; generalized ultrametric matrices; birth and death chains; Moran models; sharp strong stationary time; sharp dual

Domaines: Probabilités [math.PR]

Thierry Huillet, Servet Martinez. Duality and Intertwining for discrete Markov kernels: relations and examples. Advances in Applied Probability, 2011, 43, no 2, pp.437-460. ⟨hal-00401732⟩