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Teoriya Veroyatnostei i ee Primeneniya, 2002, Volume 47, Issue 2, Pages 402–410
DOI: https://doi.org/10.4213/tvp3673
(Mi tvp3673)
 

This article is cited in 10 scientific papers (total in 10 papers)

Short Communications

Max-semistable laws in extremes of stationary random sequences

M. G. Temidoa, L. Canto E. Castrob

a University of Coimbra
b Center of Mathematics and Fundamental Applications, University of Lisbon
Abstract: In this paper we consider stationary sequences under the validity of an extension of Leadbetter's condition $D(u_n)$. For these sequences we prove that, if $\{k_n\}$ is a nondecreasing integer sequence satisfying $\lim_{n\to+\infty}k_{n+1}/k_n=r\ge 1$, then the limit law for the maximum of the first $k_n$ variables is a max-semistable law. This generalizes the corresponding result for sequences of independent identically distributed random variables of Grinevich [Theory Probab. Appl., 38 (1993), pp. 640–650] and the extremal types theorem of Leadbetter [Z. Wahrsch. Verw. Gebiete, 28 (1974), pp. 289–303]. We also prove that the limiting behavior of this maximum can be inferred from the limiting behavior of the corresponding maximum of the associated independent sequence, and we extend the well-known notion of extremal index. An illustrative example is given.
Keywords: maximum, weak convergence, stationarity, max-semistable laws.
Received: 13.05.1999
English version:
Theory of Probability and its Applications, 2003, Volume 47, Issue 2, Pages 365–374
DOI: https://doi.org/10.1137/S0040585X97979780
Bibliographic databases:
Document Type: Article
Language: English
Citation: M. G. Temido, L. Canto E. Castro, “Max-semistable laws in extremes of stationary random sequences”, Teor. Veroyatnost. i Primenen., 47:2 (2002), 402–410; Theory Probab. Appl., 47:2 (2003), 365–374
Citation in format AMSBIB
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\by M.~G.~Temido, L.~Canto E.~Castro
\paper Max-semistable laws in extremes of stationary random sequences
\jour Teor. Veroyatnost. i Primenen.
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\pages 402--410
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\zmath{https://zbmath.org/?q=an:1037.60050}
\transl
\jour Theory Probab. Appl.
\yr 2003
\vol 47
\issue 2
\pages 365--374
\crossref{https://doi.org/10.1137/S0040585X97979780}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000183800700019}
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  • https://doi.org/10.4213/tvp3673
  • https://www.mathnet.ru/eng/tvp/v47/i2/p402
  • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теория вероятностей и ее применения Theory of Probability and its Applications
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