Asymptotic formulas for the left truncated moments of sums with consistently varying distributed increments
2021 ◽
Vol 26
(6)
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pp. 1200-1212
Keyword(s):
In this paper, we consider the sum Snξ = ξ1 + ... + ξn of possibly dependent and nonidentically distributed real-valued random variables ξ1, ... , ξn with consistently varying distributions. By assuming that collection {ξ1, ... , ξn} follows the dependence structure, similar to the asymptotic independence, we obtain the asymptotic relations for E((Snξ)α1(Snξ > x)) and E((Snξ – x)+)α, where α is an arbitrary nonnegative real number. The obtained results have applications in various fields of applied probability, including risk theory and random walks.
2013 ◽
Vol 18
(4)
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pp. 519-525
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2008 ◽
Vol 45
(04)
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pp. 1196-1203
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1995 ◽
Vol 23
(2)
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pp. 938-947
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1978 ◽
Vol 15
(02)
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pp. 280-291
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Asymptotic Probabilities of an Exceedance Over Renewal Thresholds with an Application to Risk Theory
2005 ◽
Vol 42
(01)
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pp. 153-162
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