Duality and Cones of Markov Processes and Their Semigroups

M. Moehle

2013, v.19, Issue 1, 149-162

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.

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

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Laboratory of large random systems, Dept. of Mechanics and Mathematics
Moscow State University, Vorobievy Gory, 119952 Moscow Russia
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The journal was founded in 1995 by prof. Malyshev V. A.
Published by Polymat Publishing Company, Moscow, Russia
ISSN 1024-2953
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M. Moehle