Weak atomic convergence of finite voter models toward Fleming-Viot processes

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:128

Article

Chen, Yu-Ting¹  Cox, J. Theodore² 

[1] Univ Tennessee, Dept Math, Knoxville, TN 37996 USA

[2] Syracuse Univ, Dept Math, Syracuse, NY 13244 USA

关键词: Voter model;    Fleming-Viot process;    Empirical measures;    Weak atomic convergence;    Entropy;    Diversity statistics;   

DOI  :  10.1016/j.spa.2017.09.015

来源: Elsevier

【 摘 要 】

We consider the empirical measures of multi-type voter models with mutation on large finite sets, and prove their weak atomic convergence in the sense of Ethier and Kurtz (1994) toward a Fleming-Viot process. Convergence in the weak atomic topology is strong enough to answer a line of inquiry raised by Aldous (2013) concerning the distributions of the corresponding entropy processes and diversity processes for types. Published by Elsevier B.V.

【 授权许可】

Free