The strong approximation of extremal processes (II)

DOI10.1007/BF00532159zbMath0488.60031MaRDI QIDQ3949726

Paul Deheuvels

Publication date: 1983

Published in: Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete (Search for Journal in Brave)

zbMATH Keywords

extreme value distributionsmaximastrong approximationPoisson processesextremal processes

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Convergence of probability measures (60B10) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

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Doob, Ignatov and optional skipping. ⋮ Strong Approximations For It-Records And Records In TheF^α-Scheme-A Duality ⋮ Strong approximations of k-th records and k-th record times by Wiener processes ⋮ Processes of \(r^{th}\) largest ⋮ Strong approximation of the number of renewal paced record times ⋮ On independence of \(k\)-record processes: Ignatov's theorem revisited ⋮ Strong approximation of maxima by extremal processes ⋮ K-th Record Values and Their Basic Properties ⋮ The k-record processes are i.i.d. ⋮ An Estimator of the Exponent of Regular Variation Based on K-Record Values ⋮ The complete characterization of the upper and lower class of the record and inter-record times of an I.I.D. sequence ⋮ Independent Poisson processes generated by record values and inter-record times

Cites Work

• Functional limit theorems for extreme values of arrays of independent random variables
• Characterizations of probability distributions. A unified approach with an emphasis on exponential and related models
• First-order autoregressive gamma sequences and point processes
• The strong approximation of extremal processes
• A new autoregressive time series model in exponential variables (NEAR(1))
• Inverses of extremal processes
• On discrete time extremal processes
• Extremal Processes
• The structure of extremal processes
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