Open Access
October 1996 Cluster formation in a stepping-stone model with continuous, hierarchically structured sites
Steven N. Evans, Klaus Fleischmann
Ann. Probab. 24(4): 1926-1952 (October 1996). DOI: 10.1214/aop/1041903211


A stepping-stone model with site space a continuous, hierarchical group is constructed via duality with a system of (delayed) coalescing "stable" Lévy processes. This model can be understood as a continuum limit of discrete state-space, two-allele, genetics models with hierarchically structured resampling and migration. The existence of a process rescaling limit on suitably related large space and time scales is established and interpreted in terms of the dynamics of cluster formation. This paper was inspired by recent work of Klenke.


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Steven N. Evans. Klaus Fleischmann. "Cluster formation in a stepping-stone model with continuous, hierarchically structured sites." Ann. Probab. 24 (4) 1926 - 1952, October 1996.


Published: October 1996
First available in Project Euclid: 6 January 2003

zbMATH: 0871.60090
MathSciNet: MR1415234
Digital Object Identifier: 10.1214/aop/1041903211

Primary: 60K35
Secondary: 60B15 , 60J30 , 60J60

Keywords: cluster formation , clustering , coalescing Lévy process , Fisher-Wright diffusion , hierarchical structure , Interacting diffusion , Measure-valued process , migration , Resampling , stepping-stone model , Stochastic partial differential equation

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 4 • October 1996
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