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- J. Geluk, L. de Haan, S. Resnick
- 1995

Second order regular variation is a reenement of the concept of regular variation which is useful for studying rates of convergence in extreme value theory and asymptotic normality of tail estimators. For a distribution tail 1 ? F which possesses second order regular variation, we discuss how this property is inherited by 1 ? F 2 and 1 ? F 2. We also… (More)

- JAAP GELUK, GELUKAND K. W. NG
- 2006

Consider a sequence {Xk, k ≥ 1} of random variables on (−∞,∞). Results on the asymptotic tail probabilities of the quantities Sn = ∑nk=0 Xk ,X(n) = max0≤k≤n Xk , and S(n) = max0≤k≤n Sk , with X0 = 0 and n ≥ 1, are well known in the case where the random variables are independent with a heavy-tailed (subexponential) distribution. In this paper we investigate… (More)

- J. L. Geluk, Liang Peng
- 1999

for MA(l) time series J.L. Geluk Liang Peng y Econometric Institute 1 Report EI-9910-A Abstract For samples of random variables with a regularly varying tail estimating the tail index has received much attention recently. For the proof of asymptotic normality of the tail index estimator second order regular variation is needed. In this paper we rst… (More)

- Jaap Geluk, Qihe Tang
- 2008

In this paper we study the asymptotic behavior of the tail probabilities of sums of dependent and real-valued random variables whose distributions are assumed to be subexponential and not necessarily of dominated variation. We propose two general dependence assumptions under which the asymptotic behavior of the tail probabilities of the sums is the same as… (More)

- Jiusun Zeng, Uwe Kruger, Jaap Geluk, Xun Wang, Lei Xie
- Automatica
- 2014

Let X1, X2, . . . Xn be independent and identically distributed (i.i.d.) non-negative random variables with common distribution function (d.f.) F with unbounded support and EX2 1 < ∞. We show that for a large class of heavy tailed random variables with a finite variance the renewal function U satisfies U(x)− x μ − μ2 2μ2 ∼ − 1 μx ∫ ∞

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