Electronic Communications in Probability

Electronic Communications in Probability > Vol. 7 (2002) > Paper 2

Large Deviations and Quasi-Potential of a Fleming-Viot Process

Shui Feng, McMaster University
Jie Xiong, University of Tennessee

Abstract
The large deviation principle is established for the Fleming-Viot process with neutral mutation when the process starts from a point on the boundary. Since the diffusion coefficient is degenerate on the boundary, the boundary behavior of the process is investigated in detail. This leads to the explicit identification of the rate function, the quasi-potential, and the structure of the effective domain of the rate function.

Full text: PDF

Pages: 13-25

Published on: January 7, 2002

Bibliography

D. Dawson and S. Feng, Large deviations for the Fleming-Viot process with neutral mutation and selection. Stochastic Process. Appl., 77, 207-232 (1998) Math. Review 99h:60050
D. Dawson and S. Feng, Large deviations for the Fleming-Viot process with neutral mutation and selection, II. Stochastic Process. Appl., 92, 131-162. Math. Review 2001m:60060
A. Dembo and O. Zeitouni., Large deviations techniques and applications. Second edition. Applications of Mathematics, 38, Springer-Verlag, New York (1998). Math. Review 99d:60030
S.N. Ethier and T.G. Kurtz, Convergence to Fleming-Viot processes in the weak atomic topology. Stoch. Proc. Appl., 54, 1-27. (1994). Math. Review 95m:60075
H. H. Kuo, Gaussian Measures in Banach Spaces. Lecture Notes in Mathematics, 463, Springer-Verlag (1975). Math. Review 57 #1628

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Electronic Communications in Probability. ISSN: 1083-589X