Extreme values for stationary sequences

  • George L. O’Brien
Part of the Progress in Probability and Statistics book series (PRPR, volume 11)


Let (Xn) n = 1 be a strictly stationary real-valued sequence and let F(x) = P[X1 ≤ x]. Let Mi,j = max(Xi+1,..., Xj) and Mj = max(X1,...,Xj) = M0,j. Let (cn) n = 1 be a sequence of real numbers. The purpose of this article is to review the theory of the asymptotic behaviour of P[Mn ≤ cn] as n → ∞. We mainly consider aspects which are not treated in Leadbetter, Lindgren and Rootzén [4]. To avoid trivialities we assume that F(cn) < 1 for all n, F(cn) → 1, and P[X1 = sup{x: F(x) < 1}] = 0. All limits are “as n → ∞.”


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© Springer Science+Business Media New York 1986

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  • George L. O’Brien

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