The Annals of Applied Probability

Elliptic and other functions in the large deviations behavior of the Wright-Fisher process

F. Papangelou

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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.

Article information

Source
Ann. Appl. Probab., Volume 8, Number 1 (1998), 182-192.

Dates
First available in Project Euclid: 29 July 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1027961039

Digital Object Identifier
doi:10.1214/aoap/1027961039

Mathematical Reviews number (MathSciNet)
MR1620354

Zentralblatt MATH identifier
0942.60020

Subjects
Primary: 60F10: Large deviations
Secondary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) [See also 90B30, 91D10, 91D35, 91E40]

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

Citation

Papangelou, F. Elliptic and other functions in the large deviations behavior of the Wright-Fisher process. Ann. Appl. Probab. 8 (1998), no. 1, 182--192. doi:10.1214/aoap/1027961039. https://projecteuclid.org/euclid.aoap/1027961039


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References

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