Graphical Representation of some Duality Relations in Stochastic Population Models

Details Graphical Representation of some Duality Relations in Stochastic Population Models Graphical Representation of some Duality Relations in Stochastic Population Models

2007-06-26

arxiv.org/abs/0706.3852v1

Electron. Comm. Probab. 12 (2007), 206--220

Mathematics

Probability

17 pages, 3 figures

Scientific paper

We derive a unified stochastic picture for the duality of a resampling-selection model with a branching-coalescing particle process (cf. http://www.ams.org/mathscinet-getitem?mr=MR2123250) and for the self-duality of Feller's branching diffusion with logistic growth (cf. math/0509612). The two dual processes are approximated by particle processes which are forward and backward processes in a graphical representation. We identify duality relations between the basic building blocks of the particle processes which lead to the two dualities mentioned above.

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