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Limit theorems for stationary distributions

Published online by Cambridge University Press:  01 July 2016

M. Frank Norman
M. Frank Norman*
Affiliation:
University of Pennsylvania
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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.

Keywords

STATIONARY PROCESSESLIMIT THEOREMSDIFFUSION APPROXIMATIONGENETIC MODELS
Type
Research Article
Information
Advances in Applied Probability , Volume 7 , Issue 3 , September 1975 , pp. 561 - 575
Copyright
Copyright © Applied Probability Trust 1975 

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