Generalized stepping stone model with Ξ-resampling mechanism

2020/09/24 by Huili Liu, Liu, Huili, Xiaowen Zhou +1
Economics, Econometrics and Finance · Mathematics · Medicine · #60J25 #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Primary 60G57 #Probability (math.PR) #Secondary 60J35 #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:60G57 #msc:60J25 #msc:60J35

paper · pdf · doi:10.48550/arxiv.2009.11430

19 pages

openalex publication_date 2020/09/24 · arxiv created 2021/02/03 · arxiv updated 2021/02/05 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

A generalized stepping stone model with Ξ-resampling mechanism is a two dimensional probability-measure-valued stochastic process whose moment dual is similar to that of the classical stepping stone model except that Kingman's coalescent is replaced by Ξ-coalescent. We prove the existence of such a process by specifying its moments using the dual function-valued Ξ-coalescent process with geographical labels and migration, and then verifying a multidimensional Hausdorff moment problem. We also characterize the stationary distribution of the generalized stepping stone model and show that it is not reversible if the mutation operator is of uniform jump-type.

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