Duality and cones of Markov processes and their semigroups. (English) Zbl 1298.60079

Möhle, M.

Markov Process. Relat. Fields 19, No. 1, 149-162 (2013).

Author’s abstract: We show that the cone duality essentially coincides with Liggett’s definition of duality of Markov processes. Several examples, mainly motivated from mathematical population genetics, of dual Markov processes and their corresponding convex cones are provided, including Fleming-Viot measure-valued processes and their dual coalescents with simultaneous multiple collisions of ancestral lineages.

Reviewer: Marius Iosifescu (Bucureşti)

MSC:

60J25	Continuous-time Markov processes on general state spaces
60J20	Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
60K35	Interacting random processes; statistical mechanics type models; percolation theory
92D10	Genetics and epigenetics
92D25	Population dynamics (general)

Keywords:

coalescent; cone; duality; Fleming-Vior process; stochastic monotone Markov chain