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arXiv · 0706.3852

Graphical Representation of some Duality Relations in Stochastic Population Models

Roland Alkemper·Martin Hutzenthaler
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Abstract

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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Roland Alkemper, Martin Hutzenthaler. 2007-06-26. Graphical Representation of some Duality Relations in Stochastic Population Models. https://arxiv.org/abs/0706.3852

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