2005/09/16 by Xiaowen Zhou, Zhou, Xiaowen · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #60G57 #60J65 #Complex Systems and Time Series Analysis #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR #msc:60G57 #msc:60J65
paper · pdf · doi:10.48550/arxiv.math/0509383
12 pages
arxiv created 2005/09/16 · openalex publication_date 2005/09/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we consider a stepping-stone model on a circle with circular Brownian migration. We first point out a connection between Arratia flow and the marginal distribution of this model. We then give a new representation for the stepping-stone model using Arratia flow and circular coalescing Brownian motion. Such a representation enables us to carry out some explicit computation. In particular, we find the Laplace transform for the time when there is only a single type left across the circle.