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February 1998 Elliptic and other functions in the large deviations behavior of the Wright-Fisher process
F. Papangelou
Ann. Appl. Probab. 8(1): 182-192 (February 1998). DOI: 10.1214/aoap/1027961039

Abstract

The present paper continues the work of two previous papers on the variational behavior, over a large number of generations, of a Wright-Fisher process modelling an even larger reproducing population. It was shown that a Wright-Fisher process subject to random drift and one-way mutation which undergoes a large deviation follows with near certainty a path which can be a trigonometric, exponential, hyperbolic or parabolic function. Here it is shown that a process subject to random drift and gamete selection follows in similar circumstances a path which is, apart from critical cases, a Jacobian elliptic function.

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F. Papangelou. "Elliptic and other functions in the large deviations behavior of the Wright-Fisher process." Ann. Appl. Probab. 8 (1) 182 - 192, February 1998. https://doi.org/10.1214/aoap/1027961039

Information

Published: February 1998
First available in Project Euclid: 29 July 2002

zbMATH: 0942.60020
MathSciNet: MR1620354
Digital Object Identifier: 10.1214/aoap/1027961039

Subjects:
Primary: 60F10
Secondary: 60J20

Keywords: action functional , calculus of variations , elliptic functions , large deviations , Wright-Fisher process

Rights: Copyright © 1998 Institute of Mathematical Statistics

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Vol.8 • No. 1 • February 1998
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