Duality and Intertwining for discrete Markov kernels: a relation and examples

2009/07/05 by Thierry Huillet, Huillet, Thierry, Servet Martı́nez +2 · 1 citation
Mathematics · #60J10 #60J70 #60J80 #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #advanced mathematical theories #math.PR #msc:60J10 #msc:60J70 #msc:60J80

paper · pdf · doi:10.48550/arxiv.0907.0840

arxiv created 2009/07/05 · openalex publication_date 2009/07/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• Markov dualities via the spectral decompositions of the two Markov generators in their bi-orthogonal basis of right and left eigenvectors

Related

• Intertwining and Duality for Consistent Markov Processes
• Truncation in Duality and Intertwining Kernels
• On the notion(s) of duality for Markov processes
• On the Markov commutator
• Duality theory for Markov processes: Part 1