Asympyotic expansions for infinite weighted convolutions of light subexponential distributions

The finite-time ruin probability of the nonhomogeneous Poisson risk model with conditionally independent subexponential claims

This paper obtains an asymptotic formula for the finite-time ruin probability of the compound nonhomogeneous Poisson risk model with a constant interest force, in which the claims are conditionally independent random variables with a common subexponential distribution. The paper also obtains some asymptotic relations of randomly weighted sums $\sum_{i=1}^n θ_iX_i$, in which the weights $θ_i$ $i=1,2,\cdots, n$ are positive random variables which are bounded above and the primary random variables $X_i$, $i=1,2,\cdots,n$ are conditionally independent and follow subexponential distributions.

Second order subexponentiality and infinite divisibility

We characterize the second order subexponentiality of an infinitely divisible distribution on the real line under an exponential moment assumption. We investigate the asymptotic behaviour of the difference between the tails of an infinitely divisible distribution and its Lévy measure. Moreover, we study the second order asymptotic behaviour of the tail of the $t$-th convolution power of an infinitely divisible distribution. The density version for a self-decomposable distribution on the real line without an exponential moment assumption is also given. Finally, the regularly varying case for a …

Two hypotheses on the exponential class in the class of $O$-subexponential infinitely divisible distributions

Two hypotheses on the class $\mathcal{L}(γ)$ in the class $\mathcal{OS}\cap \mathcal{ID}$ are discussed. Two weak hypotheses on the class $\mathcal{L}(γ)$ in the class $\mathcal{OS}\cap \mathcal{ID}$ are proved. A necessary and sufficient condition in order that, for every $t >0$, the $t$-th convolution power of a distribution in the class $\mathcal{OS}\cap \mathcal{ID}$ belongs to the class $\mathcal{L}(γ)$ is given.

On subexponentiality of the Lévy measure of the diffusion inverse local time; with applications to penalizations

For a recurrent linear diffusion on $\R_+$ we study the asymptotics of the distribution of its local time at 0 as the time parameter tends to infinity. Under the assumption that the Lévy measure of the inverse local time is subexponential this distribution behaves asymtotically as a multiple of the Lévy measure. Using spectral representations we find the exact value of the multiple. For this we also need a result on the asymptotic behavior of the convolution of a subexponential distribution and an arbitrary distribution on $\R_+.$ The exact knowledge of the asymptotic behavior of the distribut…

正递减分布及其相关分布类在相依性下的闭包性质

Closure properties in positively decreasing and related distributions under dependence

本文研究正递减分布类在不同相依结构下的闭包性质，涵盖最小、最大、卷积等运算，并引入广义长尾正递减分布类，探讨随机停止和的封闭性及随机向量的闭包性质。

The conjectures of Embrechts and Goldie

It is shown that the class of convolution equivalent distributions and the class of locally subexponential distributions are not closed under convolution roots. Moreover, two sufficient conditions for the closure under convolution roots of the class of convolution equivalent distributions are given.

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

We establish some asymptotic expansions for infinite weighted convolution of distributions having regular varying tails. Various applications to statistics and probability are developed.

Tail asymptotics for the supremum of a random walk when the mean is not finite

We consider the sums $S_n=ξ_1+\cdots+ξ_n$ of independent identically distributed random variables. We do not assume that the $ξ$'s have a finite mean. Under subexponential type conditions on distribution of the summands, we find the asymptotics of the probability ${\bf P}\{M>x\}$ as $x\to\infty$, provided that $M=\sup\{S_n,\ n\ge1\}$ is a proper random variable. Special attention is paid to the case of tails which are regularly varying at infinity. We provide some sufficient conditions for the integrated weighted tail distribution to be subexponential. We supplement these conditions by a numbe…

多维再保险模型的均匀渐进行为：具有随机延迟索赔数量和多变量亚指数性

Uniform asymptotics for a multidimensional renewal risk model with random number of delayed claims and multivariate subexponentiality

本文研究了具有共同再保险计数过程、恒定利率的多维风险模型，探讨了在有限和无限时间范围内，折现累计索赔进入稀有集的概率渐进行为，考虑了主索赔和延迟索赔的亚指数尾部渐近等价性及延迟索赔的次要性，提供了局部均匀估计和更明确的公式。

具有常利息力的连续时间更新风险模型中贴现总索赔的二阶渐近性

Second order asymptotics for discounted aggregate claims of continuous-time renewal risk models with constant interest force

针对含常利息力的连续时间更新风险模型，论文利用随机加权和的二阶次指数渐近理论与加权 Kesten 型不等式，建立了贴现总索赔尾概率的二阶渐近公式。

Some positive conclusions related to the Embrechts-Goldie' conjecture

In this paper, we give some conditions, under which, if an infinitely divisible distribution supported on $[0,\infty)$ belongs to the intersection of exponential distribution class $\mathcal{L}(γ)$ for some $γ\ge0$ and generalised subexponential distribution class $\mathcal{OS}$, then its L$\rm\acute{e}$vy spectral distribution or convolution of the distribution with itself also belongs to the same one. To this end, we discuss the closure under the compound convolution roots for the class. In addition, we do some in-depth discussion about the above-mentioned conditions, and provide some types …

二维随机加权和尾部概率的二阶渐近分析

Second-order Asymptotic Analysis of Tail Probabilities of Bidimensional Randomly Weighted Sums

研究保险二维离散时间风险模型中总净损失随机折现价值两类尾部概率的二阶渐近性，通过建立随机加权和公式并应用于模型，得到二阶渐近公式，数值模拟显示其比一阶更精确。

关于Talagrand卷积猜想的一些注记

Some remarks on Talagrand's convolution conjecture

本文通过鞅方法，利用停止密度鞅和加权伊藤等距估计，为高斯和布尔设定下的Talagrand卷积猜想提供了带显式无维常数的自包含证明。