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The almost sure central limit theorems in the joint version for the maxima and sums of certain stationary Gaussian sequences

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  • Dudzinski, Marcin

Abstract

Suppose that X1,X2,... is a standardized stationary Gaussian sequence. Let: Mn:=max(X1,...,Xn), , , and an>0, bn denote suitable normalizing constants. Our goal is to prove the almost sure central limit theorem for the sequence {an(Mn-bn),Sn/[sigma]n}, under certain additional assumptions on the covariance function r(t):=Cov(X1,X1+t).

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  • Dudzinski, Marcin, 2008. "The almost sure central limit theorems in the joint version for the maxima and sums of certain stationary Gaussian sequences," Statistics & Probability Letters, Elsevier, vol. 78(4), pages 347-357, March.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:4:p:347-357
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    References listed on IDEAS

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    1. Csáki, Endre & Gonchigdanzan, Khurelbaatar, 2002. "Almost sure limit theorems for the maximum of stationary Gaussian sequences," Statistics & Probability Letters, Elsevier, vol. 58(2), pages 195-203, June.
    2. Bagai, Isha & Prakasa Rao, B. L. S., 1991. "Estimation of the survival function for stationary associated processes," Statistics & Probability Letters, Elsevier, vol. 12(5), pages 385-391, November.
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