Limit theorems for stationary distributions

descriptionPublicationkeyboard_double_arrow_right Article 01 Sep 1975 English Publisher:Cambridge University Press (CUP)Journal:Advances in Applied Probability, volume 7, pages 561-575 (issn: 0001-8678, eissn: 1475-6064,

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Authors: Norman, M. Frank;

doi: 10.2307/1426128

Limit theorems for stationary distributions

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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 τ N are positive null sequences. Limiting distributions of as N → ∞ are obtained for the cases τ N = ∊ N and τ N = 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.

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University of Pennsylvania
United States

Keywords

Stationary stochastic processes, Central limit and other weak theorems, Genetics and epigenetics, Diffusion processes

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