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

Marcin Dudzinski

Statistics & Probability Letters, 2008, vol. 78, issue 4, 347-357

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).

Keywords: Almost; sure; central; limit; theorem; Extreme; values; Partial; sums; Stationary; Gaussian; sequences; Associated; random; variables; Slowly; varying; functions; at; infinity; Karamata's; theorem (search for similar items in EconPapers)
Date: 2008
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