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• W1570487082 abstract "Consider a system X = ((x�(t)),� 2 N)t�0 of interacting Fleming-Viot diffusions with mutation and selection which is a strong Markov process with continuous paths and state space (P(I))N, where I is the type space, N the geographic space is assumed to be a countable group and P denotes the probability measures. We establish various duality relations for this process. These dualities are function-valued processes which are driven by a coalescing-branching random walk, that is, an evolving particle system which in addition exhibits certain changes in the function-valued part at jump times driven by mutation. In the case of a finite type space I we construct a set-valued dual process, which is a Markov jump process, which is very suitable to prove ergodic theorems which we do here. The set-valued duality contains as special case a duality relation for any finite state Markov chain. In the finitely many types case there is also a further tableau-valued dual which can be used to study the invasion of fitter types after rare mutation. This is carried out in [DGsel] and [DGInvasion]." @default.
• W1570487082 created "2016-06-24" @default.
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• W1570487082 date "2011-04-06" @default.
• W1570487082 modified "2023-09-27" @default.
• W1570487082 title "Duality for spatially interacting Fleming-Viot processes with mutation and selection" @default.
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