Graphical Representation of some Duality Relations in Stochastic Population Models
Probability
2009-04-16 v1
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.
Cite
@article{arxiv.0706.3852,
title = {Graphical Representation of some Duality Relations in Stochastic Population Models},
author = {Roland Alkemper and Martin Hutzenthaler},
journal= {arXiv preprint arXiv:0706.3852},
year = {2009}
}