Large deviations for the Fleming–Viot process with neutral mutation and selection, II

• Published in: Stochastic processes and their applications Vol. 92; no. 1; pp. 131 - 162
• Main Authors: A. Dawson, Donald, Feng, Shui
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.03.2001; Elsevier Science; Elsevier
• Series: Stochastic Processes and their Applications
• Subjects: Exact sciences and technology; Fleming-Viot process Large deviations Weak and [tau]-topology; Fleming–Viot process; Large deviations; Limit theorems; Mathematics; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Weak and τ-topology; secondary 92D10; Fleming–Viot process; Large deviations; primary 60F10; Weak and τ-topology; Selection; Neutral mutation; Fleming Viot process; Population dynamics; Sigma algebra; Mutation; Stochastic process; Dirac measure; Tau topology; Probability measure; Large deviation
• ISSN: 0304-4149; 1879-209X
• DOI: 10.1016/S0304-4149(00)00070-3

Large deviation principles are established for the Fleming–Viot process with neutral mutation and with selection, and the associated equilibrium measures as the sampling rate approaches zero and when the state space is equipped with the weak topology. The path-level large deviation results improve the results of Dawson and Feng (1998, Stochastic Process. Appl. 77, 207–232) in three aspects: the state space is more natural, the initial condition is relaxed, and a large deviation principle is established for the Fleming–Viot process with selection. These improvements are achieved through a detailed study of the behaviour near the boundary of the Fleming–Viot process with finite types.