关于马尔可夫更新测度的一个局部等价式

考虑了逗留时间服从一类次指数分布的马尔可夫更新过程,延伸了文[3]的结果,得到了马尔可夫更新测度的一个局部等价式.     

关于马尔可夫更新定理的若干局部渐近结果

在文[3]的基础上,考虑了逗留时间服从Δ-次指数分布的马尔可夫更新测度的局部渐近表达式,同时推广了关键更新定理.     

重尾索赔下双复合Poisson模型的赤字分布

本文研究重尾索赔下的双复合Poisson模型,当索赔额分布属于次指数分布类时,给出了破产在有限时间内发生赤字尾概率的一个渐近表达式.     

局部次指数分布的一类卷积封闭性的等价条件及应用

给出了支撑在[0,∞)的局部次指数分布的一类卷积封闭性的若干等价条件,并在适当的条件下推广到了全空间.在此基础上,得到了对称化分布的局部渐近性的结果.上述结果可以蕴涵Embrechts和Goldie(1980)[1]及Geluk(2004)[2]非局部的相应结果,其中部分证明比[2]简单.     

多重延迟的关键更新定理及其在风险理论中的应用

利用广义局部次指数分布族的性质,讨论了带有多重延迟且Lundberg指数不存在时的关键更新定理,所得结果包含了重尾和轻尾的情形.将此结果应用到平稳更新风险模型,得到了该模型在破产时亏损额分布的局部渐近性质.     

Farlie-Gumbel-Morgenstern联合分布的Max-Sum局部等价式

设n个随机变量服从Farlie-Gumbel-Morgenstern联合分布,本文分别研究它们的和与最大值的局部渐近性.进而,在这些随机变量服从局部次指数分布的条件下,得到Max-Sum局部等价式.该等价式从局部和相依的角度刻画了随机游动的一个大跳原理.     

一类患病阶段服从非指数分布的SEITR传染病模型的潜在假设和稳定性分析

建立了一类SEITR传染病模型,推导出模型潜在的假设条件,并得到了一般分布下相应的积分微分方程.进而,通过在疾病传播的特定阶段引入Gamma分布和指数分布将积分微分方程化简成了ODE方程,证明了服从指数分布的ODE方程的无病平衡点的局部和全局稳定性.对两类模型的控制再生数进行敏感度分析的结果表明传染率β是影响疾病传播的最重要因素.     

股票收益率的次指数分布拟合

股票收益率等金融时间序列具有重尾特征,因而不适于用正态分布来描述,次指数分布族S是一类重尾分布族,能够很好的处理具有偏态、重尾特征的金融时间序列,本文对上证指数的收益率进行了次指数分布拟合,并给出了在险价值(VaR)的估计。     

一类常见次指数族的充分条件和必要条件

本文利用Cline和Samorodnitsky(1994)的方法,讨论了长尾分布族及其相关分布族的若干性质,在此基础上,分别获得了一类次指数分布族及其相关的分布族的充分条件和必要条件.     

布朗运动和次分数布朗运动混合的局部时

本文研究了布朗运动和次分数布朗运动混合的局部时问题.利用白噪声分析方法和次分数布朗运动的另一种表示形式,证明了该局部时是一个Hida广义泛函.进一步,借助于S-变换给出了该局部时的混沌表示.最后获得了该局部时的正则性条件.推广了布朗运动局部时的一些结果.     

On Subexponential Distributions and Asymptotics of the Distribution of the Maximum of Sequential Sums

We study the properties of subexponential distributions and find new sufficient and necessary conditions for membership in the class of these distributions. We establish a connection between the classes of subexponential and semiexponential distributions and give conditions for preservation of the asymptotics of subexponential distributions for functions of distributions. We address similar problems for the class of the so-called locally subexponential distributions. As an application of these results, we refine the asymptotics of the distribution of the supremum of sequential sums of random variables with negative drift, in particular, local theorems.     

The asymptotic estimate for the sum of two correlated classes of discounted aggregate claims with heavy tails

Consider a risk model with two correlated classes of insurance business and a constant force of interest. We assume that the correlation comes from a common shock and that the claim-size distribution is heavy-tailed. Under this setting, we investigate the tail behavior of the sum of the two correlated classes of discounted aggregate claims. We obtain the uniform asymptotic formulas for some subclass of subexponential distributions.     

Random matrices and subexponential operator spaces

We introduce and study a generalization of the notion of exact operator space that we call subexponential. Using Random Matrices we show that the factorization results of Grothendieck type that are known in the exact case all extend to the subexponential case, but we exhibit (a continuum of distinct) examples of non-exact subexponential operator spaces, as well as a C*-algebra that is subexponential with constant 1 but not exact. We also show that OH, R + C and max(?₂) (or any other maximal operator space) are not subexponential.     

Tail asymptotics for the queue length in an M/G/1 retrial queue

In this paper, we study the tail behavior of the stationary queue length of an M/G/1 retrial queue. We show that the subexponential tail of the stationary queue length of an M/G/1 retrial queue is determined by that of the corresponding M/G/1 queue, and hence the stationary queue length in an M/G/1 retrial queue is subexponential if the stationary queue length in the corresponding M/G/1 queue is subexponential. Our results for subexponential tails also apply to regularly varying tails, and we provide the regularly varying tail asymptotics for the stationary queue length of the M/G/1 retrial queue. AMS subject classifications: 60J25, 60K25     

On the periodic KdV equation in weighted Sobolev spaces

We prove well-posedness results for the initial value problem of the periodic KdV equation as well as Kam type results in classes of high regularity solutions. More precisely, we consider the problem in weighted Sobolev spaces, which comprise classical Sobolev spaces, Gevrey spaces, and analytic spaces. We show that the initial value problem is well posed in all spaces with subexponential decay of Fourier coefficients, and ‘almost well posed’ in spaces with exponential decay of Fourier coefficients.     

Direct and inverse theorems of approximate methods for the solution of an abstract Cauchy problem

We consider an approximate method for the solution of the Cauchy problem for an operator differential equation based on the expansion of the exponential function in orthogonal Laguerre polynomials. For an initial value of finite smoothness with respect to the operator A, we prove direct and inverse theorems of the theory of approximation in the mean and give examples of the unimprovability of the corresponding estimates in these theorems. We establish that the rate of convergence is exponential for entire vectors of exponential type and subexponential for Gevrey classes and characterize the corresponding classes in terms of the rate of convergence of approximation in the mean. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 6, pp. 838–852, June, 2007.     

Conditional distribution of heavy tailed random variables on large deviations of their sum

It is known that large deviations of sums of subexponential random variables are most likely realised by deviations of a single random variable. In this article we give a detailed picture of how subexponential random variables are distributed when a large deviation of the sum is observed.