Duality and Cones of Markov Processes and Their Semigroups

M. Moehle

2013, v.19, №1, 149-162


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.

Keywords: coalescent,cone,duality,Fleming - Viot process,stochasticmonotone Markov chain


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