Statistics Seminars: Long time behaviour and diffusion limit of a model of interacting populations
8 October 2012 14:00 in CM221
We consider a model of interacting populations. The case of two interacting populations is modelled by an inhomogeneous random walk in the quarter-plane. If there are more than two populations, then the model is formulated in terms of a Markov birth-and-death process with local interaction. We discuss the long-time behaviour and describe a diffusion limit of the model. The diffusion approximation is given by a Markov process formed by a collection of positive interacting diffusions (given by reflected Ornstein-Uhlenbeck processes in a particular case). We also discuss the equilibrium distributions (forming a class of Gibbs measures) of both the model and its diffusion limit in the ergodic reversible case.
The talk is based on joint work with O.Hryniv and M.Menshikov.
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