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Limit theorems for stationary distributions

Published online by Cambridge University Press:  01 July 2016

M. Frank Norman*
Affiliation:
University of Pennsylvania

Abstract

For every N ≧ 1, let be a real-valued stationary process, and let . Suppose that and var, where N and τN are positive null sequences. Limiting distributions of as N are obtained for the cases τN = N and τN = o(N). These results are established by an extension of a method due to Moran. The theory is illustrated by a variety of applications to genetic models.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 1975 

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