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May, 1983 Stable Limits for Partial Sums of Dependent Random Variables
Richard A. Davis
Ann. Probab. 11(2): 262-269 (May, 1983). DOI: 10.1214/aop/1176993595


Let $\{X_n\}$ be a stationary sequence of random variables whose marginal distribution $F$ belongs to a stable domain of attraction with index $\alpha, 0 < \alpha < 2$. Under the mixing and dependence conditions commonly used in extreme value theory for stationary sequences, nonnormal stable limits are established for the normalized partial sums. The method of proof relies heavily on a recent paper by LePage, Woodroofe, and Zinn which makes the relationship between the asymptotic behavior of extreme values and partial sums exceedingly clear. Also, an example of a process which is an instantaneous function of a stationary Gaussian process with covariance function $r_n$ behaving like $r_n \log n \rightarrow 0$ as $n \rightarrow \infty$ is shown to satisfy these conditions.


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Richard A. Davis. "Stable Limits for Partial Sums of Dependent Random Variables." Ann. Probab. 11 (2) 262 - 269, May, 1983.


Published: May, 1983
First available in Project Euclid: 19 April 2007

zbMATH: 0511.60021
MathSciNet: MR690127
Digital Object Identifier: 10.1214/aop/1176993595

Primary: 60F05
Secondary: 60G10 , 60G15

Keywords: Extreme values , Gaussian processes , mixing conditions , Stable distributions

Rights: Copyright © 1983 Institute of Mathematical Statistics

Vol.11 • No. 2 • May, 1983
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