(D)族负象限相依随机变量和的精致大偏差

在负象限相依结构下,得到了支撵在(-∞,∞)上的(D)族随机变量非中心化以及中心化部分和的精致大偏差.同时,还在较弱的条件下,得到了相应的中心化随机和的精致大偏差.     

宽上限相依的随机变量和的精确大偏差

通过研究了长尾上的带宽上限相依的随机变量和的精确大偏差,利用经典大偏差的方法,得到了非随机和和随机和的两种渐近结果.     

D族END的随机变量和的精确大偏差

研究了非随机和的S_n=∑_i=1ⁿ X_i,n≥1的精确大偏差的问题,这里{X_i,i≥1}是服从控制变化尾分布族（D族）的非负的、END的随机变量,但不必是同分布的.在给定的一些假设条件下,得到了非随机和的渐近关系,推广了相应的独立同分布情形下的结论.     

多元模型的长尾相依大偏差的下界

研究了在多元模型中的服从长尾分布且带有负相依的随机变量和的尾概率,在给定的一些条件下通过采用多元大偏差的方法得到了随机变量的非随机和和随机和的大偏差的下界,推广了相应的独立同分布情形下的结论.     

相依随机变量阵列加权和的矩完全收敛性

本文研究了相依随机变量阵列加权和的矩完全收敛性.利用矩不等式和截尾法,建立了相依随机变量阵列加权和的矩完全收敛性的充分条件.将Volodin等(2004)及陈平炎等(2006)的关于独立随机变量阵列的结果推广到了负相协和负相依随机变量阵列的情形,推广并完善了Sung(2011),吴群英(2012)及郭明乐和祝东进(2012)的结果.     

长尾宽上限相依的不同分布的随机变量和的精确大偏差

研究了服从长尾分布族上的随机变量和的精确大偏差问题,其中假设代表索赔额的随机变量序列是一列宽上限相依的、不同分布的随机变量序列。在给定一些假设条件下,得到了部分和与随机和的两种一致渐近结论。     

一类负相伴随机阵列部分和的精致大偏差

本文在一些适当的条件下得到了多风险模型中负相伴随机阵列的精致大偏差,推广了一些已知的结果,同时表明在多风险模型中负相伴结构对精致大偏差同样不具有敏感性.     

负相协随机变量非随机和的差的精确大偏差

In this paper,we study precise large deviation for the non-random difference sum from j=1 to n_1(t) X_(1j)-sum from j=1 to n_2(t) X_(2j),where sum from j=1 to n_1(t) X_(1j) is the non-random sum of {X_(1j),j≥1} which is a sequence of negatively associated random variables with common distribution F_1(x),and sum from j=1 to n_2(t) X_(2j) is the non-random sum of {X_(2j),j≥1} which is a sequence of independent and identically distributed random variables,n_1(t) and n_2(t) are two positive integer functions.Under some other mild conditions,we establish the following uniformly asymptotic relation lim t→∞ sup x≥r(n_1(t))~(p+1)|(P(∑~(n_1(t)_(j=1)X_(1j)-∑~(n_2(t)_(j=1)X_(2j)-(μ_1n_1(t)-μ_2n_2(t)x))/(n_1(t)F_1(x))-1|=0.     

L族END的多元部分和的精确大偏差下界

从保险的实际出发,研究服从长尾分布族(L族)上的多元风险模型中随机变量序列的部分和的精确大偏差,其中假设随机变量序列是一列延拓负相依(END)的、同分布的随机变量序列,利用基于求L族的精确大偏差的方法得到了随机变量部分和的渐近下界.     

复合更新风险模型中负相依索赔额下的精细大偏差（英文）

本文考虑了在复合更新风险模型当中,负相依索赔额情形下与之相关的精细大偏差的若干问题.文中假设{X_n,n≥1}是一列负相依的随机变量,其对应分布列为{F_n,n≥1},并假定F_n的右尾分布等同于某个具有一致变化尾的分布.根据所得的结果试图建立与经典大偏差相似的结论,并将其应用到改进后的复合更新风险模型当中.     

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??In this paper, precise large deviations of nonnegative, non-identical distributions and negatively associated random variables are investigated. Under certain conditions, the lower bound of the precise large deviations for the non-random sum is solved and the uniformly asymptotic results for the corresponding random sum are obtained. At the same time, we deeply discussed the compound renewal risk model, in which we found that the compound renewal risk model can be equivalent to renewal risk model under certain conditions. The relative research results of precise large deviations are applied to the more practical compound renewal risk model, and the theoretical and practical values are verified. In addition, this paper also shows that the impact of this dependency relationship between random variables to precise large deviations of the final result is not significant.     

Complete Convergence for Weighted Sums of Negatively Superadditive Dependent Random Variables

Let $\{X_n,n\geq1\}$ be a sequence of negatively superadditive dependent (NSD, in short) random variables and $\{a_{nk}, 1\leq k\leq n, n\geq1\}$ be an array of real numbers. Under some suitable conditions, we present some results on complete convergence for weighted sums $\sum_{k=1}^na_{nk}X_k$ of NSD random variables by using the Rosenthal type inequality. The results obtained in the paper generalize some corresponding ones for independent random variables and negatively associated random variables.     

负相关随机变量加权和的强定律(英文)

在本文中我们讨论了不同分布负相关随机变量加权和的强定律.在一个有限矩生成函数的条件下,一些有关负相关随机变量加权和的强定律被获得.这些结果推广了Soo HakSung[4]关于独立同分布随机变量的相应结论.我们的结果也概括了Mi Hwa Ko和Tae SungKim[7]获得的相关结论,同时使得Nili Sani H R和Bozorgnia A[9]所取得的结果更加形象.     

Large Deviations for Sums of Independent Heavy-Tailed Random Variables

We obtain precise large deviations for heavy-tailed random sums , of independent random variables. are nonnegative integer-valued random variables independent of r.v. (X _i )i N with distribution functions F _i. We assume that the average of right tails of distribution functions F _i is equivalent to some distribution function with regularly varying tail. An example with the Pareto law as the limit function is given.     

Precise Large Deviations for Sums of Negatively Associated Random Variables with Common Dominatedly Varying Tails

In this paper, we obtain results on precise large deviations for non-random and random sums of negatively associated nonnegative random variables with common dominatedly varying tail distribution function. We discover that, under certain conditions, three precise large-deviation prob- abilities with different centering numbers are equivalent to each other. Furthermore, we investigate precise large deviations for sums of negatively associated nonnegative random variables with certain negatively dependent occurrences. The obtained results extend and improve the corresponding results of Ng, Tang, Yan and Yang （J. Appl. Prob., 41, 93-107, 2004）.     

Asymptotic Expansions of Large Deviations for Sums of Nonidentically Distributed Random Variables

The work is designated for obtaining asymptotic expansions and determination of structures of the remainder terms that take into consideration large deviations both in Cramer zones and Linnik power zones for the distribution function of sums of independent nonidentically distributed random variables (r.v.). In this scheme of summation of r.v., the results are obtained first by mainly using the general lemma on large deviations considering asymptotic expansions for an arbitrary r.v. with regular behaviour of its cumulants [11]. Asymptotic expansions in the Cramer zone for the distribution function of sums of identically distributed r.v. were investigated in the works [1,2]. Note that asymptotic expansions for large deviations were first obtained in the probability theory by J. Kubilius [3].     

Local Precise Large and Moderate Deviations for Sums of Independent Random Variables

Let {X, X_k : k ≥ 1} be a sequence of independent and identically distributed random variables with a common distribution F. In this paper, the authors establish some results on the local precise large and moderate deviation probabilities for partial sums S_n =sum from i=1 to n(X_i) in a unified form in which X may be a random variable of an arbitrary type,which state that under some suitable conditions, for some constants T 0, a and τ 1/2and for every fixed γ 0, the relation P(S_n- na ∈(x, x + T ]) ~nF((x + a, x + a + T ]) holds uniformly for all x ≥γn~τ as n→∞, that is, P(Sn- na ∈(x, x + T ]) lim sup- 1 = 0.n→+∞x≥γnτnF((x + a, x + a + T ])The authors also discuss the case where X has an infinite mean.