Extremes of order statistics of stationary Gaussian processes

• Autorzy: Zhao C.

Identyfikatory

DOI

10.19195/0208-4147.38.1.4

• Języki publikacji: EN

Abstrakty

EN

Let {X_i(t), t ≥ 0}, 1 ≤ i ≤ n, be mutually independent and identically distributed centered stationary Gaussian processes. Under some mild assumptions on the covariance function, we derive an asymptotic expansion of P [formula] ]X_(r) (t) ≤ u) as u → ∞, where m_r(u) = (P([formula] X_(r) (t) > u))⁻¹ (1 + o(1)), and {X_(r) (t), t ≥ 0} is the rth order statistic process of {X_i(t), t ≥ 0}, 1 ≤ i, r ≤ n. As an application of the derived result, we analyze the asymptotics of supremum of the order statistic process of stationary Gaussian processes over random intervals.

Słowa kluczowe

EN

asymptotic; Gaussian processes; order statistic; stationarity; supremum

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2018
• Tom: Vol. 38, Fasc. 1
• Strony: 61--75
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Zhao C.

• Department of Statistics, School of Mathematics, Southwest Jiaotong University, Xi’an Road 999, Xipu, Pixian, Chengdu, Sichuan 611756, PR of China

Bibliografia

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).