DARWINIAN EVOLUTION AS BROWNIAN MOTION ON THE SIMPLEX: A GEOMETRIC PERSPECTIVE ON STOCHASTIC REPLICATOR DYNAMICS

• 成果类型: Article
• 署名作者: Lehmann, Tobias
• 署名单位: Leipzig University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1817
• 发表日期: 2023
• 页码: 344-375
• 关键词: statistical-analysis; EQUATIONS; distance

摘要

We prove that stochastic replicator dynamics can be interpreted as intrin-sic Brownian motion on the simplex equipped with the Aitchison geometry. As an immediate consequence, we derive three approximation results in the spirit of Wong-Zakai approximation, Donsker's invariance principle and a JKO-scheme. Using the Fokker-Planck equation and Wasserstein-contraction estimates, we also study the long time behavior of the stochastic replicator equation, as an example of a nongradient drift diffusion on the Aitchison simplex.