Ergodic behaviour of extreme values

S. Cheng; L. Peng; Y. Qi

doi:10.1017/s1446788700001932

Ergodic behaviour of extreme values

S. Cheng^*, L. Peng, Y. Qi

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

Let {X_n, n ≥ 1} be independent identically distributed random variables with a common non-degenerate distribution function F. For each n ≥ 1, denote M_n = max{X₁, . . . , X_n}. Under certain conditions on F, there exist constants a_n > 0 and b_n ∈ ℝ such that (M_n - b_n)/a_n →^d G. In this paper, we shall show that {(M_n - b_n)/a_n} exhibits ergodic behaviour under additional conditions on F.

Original language	English
Pages (from-to)	170-180
Number of pages	11
Journal	Journal of the Australian Mathematical Society
Volume	68
Issue number	2
DOIs	https://doi.org/10.1017/s1446788700001932
Publication status	Published - Apr 2000
Externally published	Yes

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10.1017/s1446788700001932

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title = "Ergodic behaviour of extreme values",

abstract = "Let {Xn, n ≥ 1} be independent identically distributed random variables with a common non-degenerate distribution function F. For each n ≥ 1, denote Mn = max{X1, . . . , Xn}. Under certain conditions on F, there exist constants an > 0 and bn ∈ ℝ such that (Mn - bn)/an →d G. In this paper, we shall show that {(Mn - bn)/an} exhibits ergodic behaviour under additional conditions on F.",

keywords = "Almost sure convergence, Ergodic behaviour, Extreme values, Logarithmic means",

author = "S. Cheng and L. Peng and Y. Qi",

year = "2000",

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language = "English",

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journal = "Journal of the Australian Mathematical Society",

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T1 - Ergodic behaviour of extreme values

AU - Cheng, S.

AU - Peng, L.

AU - Qi, Y.

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N2 - Let {Xn, n ≥ 1} be independent identically distributed random variables with a common non-degenerate distribution function F. For each n ≥ 1, denote Mn = max{X1, . . . , Xn}. Under certain conditions on F, there exist constants an > 0 and bn ∈ ℝ such that (Mn - bn)/an →d G. In this paper, we shall show that {(Mn - bn)/an} exhibits ergodic behaviour under additional conditions on F.

AB - Let {Xn, n ≥ 1} be independent identically distributed random variables with a common non-degenerate distribution function F. For each n ≥ 1, denote Mn = max{X1, . . . , Xn}. Under certain conditions on F, there exist constants an > 0 and bn ∈ ℝ such that (Mn - bn)/an →d G. In this paper, we shall show that {(Mn - bn)/an} exhibits ergodic behaviour under additional conditions on F.

KW - Almost sure convergence

KW - Ergodic behaviour

KW - Extreme values

KW - Logarithmic means

UR - http://www.scopus.com/inward/record.url?scp=0039030450&partnerID=8YFLogxK

U2 - 10.1017/s1446788700001932

DO - 10.1017/s1446788700001932

M3 - Article

SN - 1446-7887

VL - 68

SP - 170

EP - 180

JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

IS - 2

ER -

Ergodic behaviour of extreme values

Abstract

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