Functions of probability measures

Chover, Joshua; Ney, Peter; Wainger, Stephen

doi:10.1007/bf02790433

Cited by 268 publications

(197 citation statements)

References 2 publications

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“…It was proven in Chistyakov [5] for sufficiently small values of A and then in Chover, Ney and Wainger [6,7] for any A < 1 that EZ(t) ∼ F (t)/(1 − A) as t → ∞, provided F is subexponential. The local asymptotics were considered in Asmussen, Foss and Korshunov [2].…”

Section: Ez(t) = (1 − A)mentioning

confidence: 98%

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On lower limits and equivalences for distribution tails of randomly stopped sums

Denisov¹,

Foss²,

Korshunov³

2008

Bernoulli

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For a distribution F * τ of a random sum Sτ = ξ1 + • • • + ξτ of i.i.d. random variables with a common distribution F on the half-line [0, ∞), we study the limits of the ratios of tails F * τ (x)/F (x) as x → ∞ (here, τ is a counting random variable which does not depend on {ξn} n≥1 ). We also consider applications of the results obtained to random walks, compound Poisson distributions, infinitely divisible laws, and subcritical branching processes.

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Section: Ez(t) = (1 − A)mentioning

confidence: 98%

“…For (comments on) earlier partial results in the case τ = 2, see, for example, Chover, Ney and Wainger [6,7], Cline [8], Embrechts and Goldie [10], Foss and Korshunov [15], Pakes [19], Rogozin [20], Teugels [23] and further references therein. The proof of Theorem 3 follows from Lemmas 3 and 4 in Section 7.…”

Section: Theoremmentioning

confidence: 99%

On lower limits and equivalences for distribution tails of randomly stopped sums

Denisov¹,

Foss²,

Korshunov³

2008

Bernoulli

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“…But our technique is useful only in the transient case, for which far less is known. Chover et al (1973) provides a first order result while Grübel (1987) gives a second order formula. In the implicit case, Goldie (1991) obtained second order formulas.…”

mentioning

confidence: 99%

Asymptotic expansions for infinite weighted convolutions of heavy tail distributions and applications

Barbe¹,

McCormick²

2009

Memoirs of the AMS

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“…For the wellknown subexponential class S(0), when γ = 0, the right-hand side of (3.2) becomes 2. Since it was introduced in [3], [4], and [5], the class S(γ ) has been extensively investigated by many researchers and applied to various fields. This class is often used to model claim-size distributions; see, e.g.…”

Section: Resultsmentioning

confidence: 99%

The probabilities of absolute ruin in the renewal risk model with constant force of interest

Konstantinides

Tang

2010

J. Appl. Probab.

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In this paper we consider the probabilities of finite-and infinite-time absolute ruins in the renewal risk model with constant premium rate and constant force of interest. In the particular case of the compound Poisson model, explicit asymptotic expressions for the finite-and infinite-time absolute ruin probabilities are given. For the general renewal risk model, we present an asymptotic expression for the infinite-time absolute ruin probability. Conditional distributions of Poisson processes and probabilistic techniques regarding randomly weighted sums are employed in the course of this study.

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Functions of probability measures

Cited by 268 publications

References 2 publications

On lower limits and equivalences for distribution tails of randomly stopped sums

On lower limits and equivalences for distribution tails of randomly stopped sums

Asymptotic expansions for infinite weighted convolutions of heavy tail distributions and applications

The probabilities of absolute ruin in the renewal risk model with constant force of interest

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