Results 1 to 10 of about 676 (93)
Large deviations for random walks under subexponentiality: the big-jump domain [PDF]
, 2007 For a given one-dimensional random walk $\{S_n\}$ with a subexponential step-size distribution, we present a unifying theory to study the sequences $\{x_n\}$ for which $\mathsf{P}\{S_n>x\}\sim n\mathsf{P}\{S_1>x\}$ as $n\to\infty$ uniformly for $x\ge x_n$
Denisov, D., Dieker, A. B., Shneer, V.
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Randomly Stopped Sums with Generalized Subexponential Distribution
Axioms, 2023 Let {ξ1,ξ2,…} be a sequence of independent possibly differently distributed random variables, defined on a probability space (Ω,F,P) with distribution functions {Fξ1,Fξ2,…}. Let η be a counting random variable independent of sequence {ξ1,ξ2,…}.
Jūratė Karasevičienė, Jonas Šiaulys
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Renewal theory for random variables with a heavy tailed distribution and finite variance [PDF]
, 2011 Let X-1, X-2,... X-n be independent and identically distributed (i.i.d.) non-negative random variables with a common distribution function (d.f.) F with unbounded support and EX12 < infinity.
Frenk, Hans J.B.G., Geluk, Jaap J.L
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A Renewal Shot Noise Process with Subexponential Shot Marks
Risks, 2019 We investigate a shot noise process with subexponential shot marks occurring at renewal epochs. Our main result is a precise asymptotic formula for its tail probability.
Yiqing Chen
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Asymptotic tail behavior of phase-type scale mixture distributions [PDF]
, 2015 We consider phase-type scale mixture distributions which correspond to distributions of a product of two independent random variables: a phase-type random variable $Y$ and a nonnegative but otherwise arbitrary random variable $S$ called the scaling ...
Rojas-Nandayapa, Leonardo, Xie, Wangyue
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Second order corrections for the limits of normalized ruin times in the presence of heavy tails
Stochastic Systems, 2014 In this paper we consider a compound Poisson risk model with regularly varying claim sizes. For this model in [4] an asymptotic formula for the finite time ruin probability is provided when the time is scaled by the mean excess function. In this paper
Dominik Kortschak, Søren Asmussen
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Convolution and convolution-root properties of long-tailed distributions [PDF]
, 2015 We obtain a number of new general properties, related to the closedness of the class of long-tailed distributions under convolutions, that are of interest themselves and may be applied in many models that deal with "plus" and/or "max" operations on heavy-
Foss, Sergey, Wang, Yuebao, Xu, Hui
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Asymptotics in the symmetrization inequality [PDF]
, 2003 We give a sufficient condition for i.i.d. random variables X1,X2 in order to have P{X1-X2>x} ~ P{|X1|>x} as x tends to infinity. A factorization property for subexponential distributions is used in the proof.
Geluk, J.L. (Jaap)
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General inverse problems for regular variation [PDF]
, 2013 Regular variation of distributional tails is known to be preserved by various linear transformations of some random structures. An inverse problem for regular variation aims at understanding whether the regular variation of a transformed random object is
Damek, Ewa +3 more
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Martingale approach to subexponential asymptotics for random walks [PDF]
, 2011 Consider the random walk $S_n=\xi_1+...+\xi_n$ with independent and identically distributed increments and negative mean $\mathbf E\xi=-mx), x\to\infty$ for long-tailed distributions.
Denisov, Denis, Wachtel, Vitali
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