Subexponential Densities of Infinitely Divisible Distributions on the Half-Line

Lithuanian Mathematical Journal - Abstract. We show that, under the long-tailedness of the densities of normalized Lévy measures, the densities of infinitely divisible distributions on the...     

The Rate of Convergence for Subexponential Distributions and Densities

A distribution function F on the nonnegative real line is called subexponential if lim_x(1-F ^*n (x)/(1 - F(x)) = n for all n 2, where F ^*n denotes the nfold Stieltjes convolution of F with itself. In this paper, we consider the rate of convergence in the above definition and in its density analogue. Among others we discuss the asymptotic behavior of the remainder term R _n (x) defined by R _n (x) = 1 - F*n(x) - n(1 - F(x)) and of its density analogue r_n (x) = -(R_n (x))'. Our results complement and complete those obtained by several authors. In an earlier paper, we obtained results of the form _n(x) = O(1)f(x)R(x), where f is the density of F and R(x) = ₀ ^x (1-F(y))dy. In this paper, among others we obtain asymptotic expressions of the form R _n(x)= ₂ ⁿ R₂(x) + O(1)(-f'(x))R²(x) where f' is the derivative of f.     

On the Subexponential Property of a Class of Random Variables

Mathematical Notes -     

广义次指数族的卷积根的封闭性

设F是支撑在（-∞，∞）上的分布函数．口是一个取有限个整数值的非负随机变量，F#v为F的U重卷积．在一定条件下，本文得到了如下结论：对任意0≤y〈∞，F#v∈S（y）茸F∈S（y）．特别地，若口三挖，”≥2，本文得到了支撑在（一。。，。。）上的S（y）族的卷积根的封闭性．上述所得结果推广了[2]对应结果．     

两类解析函数族的一些性质

研究两类解析函数族的性质，推广了Chichra[4]、Mocanu[5]和Obradovic[6]的一些结果。另外，也指出了S.Owa[8]的一个错误。     

一类调度系统目标函数的两个性质

以参数Dioid为数学工具,建立了一类线性摄动模型与m×n无限缓冲串行生产线状态空间模型.由状态空间模型的输出方程得到目标函数Cmax[ω,a,b]的摄动参数表达式,并证明了它的两个重要性质.     

Subexponential decay of correlations

We describe a method for proving subexponential lower bounds for correlations functions, and apply it to study decay of correlations for maps with countable Markov partitions. One result is that LS Young’s upper estimates [Y2] are optimal in many situations. Our method is based on a general result concerning the asymptotics of renewal sequences of bounded operators acting on Banach spaces, which we apply to the iterates of the transfer operator. Oblatum 14-VII-2001 & 5-VI-2002?Published online: 6 August 2002 Dedicated to B. Weiss on the occasion of his 60th birthday RID="*" ID="*"This research was supported by the Nuffield Foundation, NUF-NAL 00.     

Subexponential behaviour of the Dirichlet heat kernel

We obtain a formula for the asymptotic behaviour of the Dirichlet heat kernel for large time in terms of the survival probability of a Brownian motion, under the assumption that the latter decays subexponentially for large time. We also obtain a lower bound for the Dirichlet heat kernel for arbitrary open and connected sets in Euclidean space.     

Extremes of Subexponential Shot Noise

Asymptotic behavior of extremes of shot noise in the case of monotone response functions with unbounded support and subexponentially distributed amplitudes is considered. It is assumed that the amplitude distribution belongs to the domain of attraction of a certain maximum-stable law. The limit distribution for maxima is obtained.     

Subexponential Estimations in the Shirshov Height Theorem

We study subexponential estimates in the Shirshov height theorem. Our proof uses Latyshev’s idea of the Dilworth theorem application. G. Chelnokov proposed using this idea in the nonmultilinear case.     

Two Hypotheses on the Exponential Class in the Class Of O-subexponential Infinitely Divisible Distributions

Journal of Theoretical Probability - Two hypotheses on the class $${mathcal {L}}(gamma )$$ in the class $$mathcal {OS}cap mathcal {ID}$$ are discussed. Two weak hypotheses on the class...     

One-Shot CFTP; Application to a Class of Truncated Gaussian Densities

In this paper, we introduce a new method for perfect simulation of multivariate densities. We use One-Shot CFTP (G. Roberts and J. Rosenthal, “One-shot coupling for certain stochastic recursive sequences,” Stochastic Processes and their Applications vol. 99 pp. 195–208, 2002) together with a monotone coupler for the Gibbs sampler, and implement the algorithm within the Read-Once CFTP protocol (D. B. Wilson, “How to couple form the past using a read-once source of randomness,” Random Structures and Algorithms vol. 16(1) pp. 85–113, 2000b). We illustrate our method by simulating efficiently from high-dimensional truncated normal distributions using the Gibbs sampler. AMS 2000 Subject Classification Primary 65C40; Secondary 65C60     

Random Variable Generation Using Concavity Properties of Transformed Densities

Abstract

Algorithms are developed for constructing random variable generators for families of densities. The generators depend on the concavity structure of a transformation of the density. The resulting algorithms are rejection algorithms and the methods of this article are concerned with constructing good rejection algorithms for general densities.     

Second-Order Subexponential Behavior of Subordinated Sequences

Suppose that , , and are three discrete probability distributions related by the equation (E): , where denotes the k-fold convolution of In this paper, we investigate the relation between the asymptotic behaviors of and . It turns out that, for wide classes of sequences and , relation (E) implies that , where is the mean of . The main object of this paper is to discuss the rate of convergence in this result. In our main results, we obtain O-estimates and exact asymptotic estimates for the difference .     

On a Property of Subexponential Distributions

Let F be a distribution function (d.f.) on [0, ) with finite first moment m >0. We define the integrated tail distribution function F ₁ of F by F ₁(t)=m^-1 ₀ ^t (1- F(u))du, t0. In this paper, we obtain sufficient conditions under which implications FSF ₁S and F ₁S FS hold, where S is the class of subexponential distributions.     

Estimates for the Distributions of the Sums of Subexponential Random Variables

Let be a random walk with independent identically distributed increments . We study the ratios of the probabilities P(S _n >x) / P(₁ > x) for all n and x. For some subclasses of subexponential distributions we find upper estimates uniform in x for the ratios which improve the available estimates for the whole class of subexponential distributions. We give some conditions sufficient for the asymptotic equivalence P(S > x) E P(₁ > x) as x . Here is a positive integer-valued random variable independent of . The estimates obtained are also used to find the asymptotics of the tail distribution of the maximum of a random walk modulated by a regenerative process.     

Subexponential distributions and characterizations of related classes

LetL(),0, 0, denote the class of distributionsF satisfying

Two Questions on Local Properties

ＬｅｔＸｂｅａｓｐａｃｅ ,ａｎｄＱａｔｏｐｏｌｏｇｉｃａｌｐｒｏｐｅｒｔｙ .Ｉｆｆｏｒｅａｃｈｘ∈Ｘ ,ｔｈｅｒｅｅｘｉｓｔｓａｎｅｉｇｈｂｏｒｈｏｏｄＵｏｆｘｓｕｃｈｔｈａｔＵｈａｓｐｒｏｐｅｒｔｙＱ ,ｔｈｅｎｗｅｃａｌｌＸａｌｏｃａｌＱ ｓｐａｃｅ .　Ｄｅｆｉｎｉｔｉｏｎ 1　ＡｓｐａｃｅＸｉｓｃａｌｌｅｄθ ｒｅｆｉｎａｂｌｅ,ｉｆｆｏｒｅｖｅｒｙｏｐｅｎｃｏｖｅｒＵｏｆＸｔｈｅｒｅｅｘｉｓｔｓａｓｅｑｕｅｎｃｅ {Ｕｎ}ｏｆｏｐｅｎｒｅｆｉｎｅｍｅｎｔｓｏｆＵｓｕｃｈｔｈａｔｆｏｒｅａｃｈｘ∈Ｘ ,…     

二维随机变量函数密度的两种求法

针对一道关于二维随机变量函数求其密度的例题,给出两种求解方法,即分布函数法和雅可比行列式法.