共查询到16条相似文献,搜索用时 125 毫秒
1.
本文研究了一类独立重尾随机变量随机和S(t)∧=∑k=1^N(t)Xk,t≥0的大偏差概率,其中{N(t),t≥0}是一放大晨负整数值随机变量;{Xn,n≥1}是非负,独立随机变量序列,并与{N(t),t≥0}独立。本文的结果将{Xn,n≥1}为独立同分布情形推广到了独立不同分布情形。 相似文献
2.
进一步研究随机变量部分和与随机和的大偏差,其中S(n)=∑ni=1Xi,S(t)=∑N(t)i=1Xi(t>0).{Xn,n≥1}是一个独立同分布的随机变量(未必是非负的)序列具有共同的分布F(定义于R上)和有限期望μ=EX1.{N(t),t≥0}是一个非负的整数值的随机变量的更新计数过程且与{Xn,n≥1}相互独立.本文在假定F∈C条件下,进一步推广并改进了由Klüppelberg等和Kaiw等人给出的一些大偏差结果.这些结果可应用到某些金融保险方面的一些特定的问题中去. 相似文献
3.
We prove large deviation results on the partial and random sums Sn = ∑i=1n Xi,n≥1; S(t) = ∑i=1N(t) Xi, t≥0, where {N(t);t≥0} are non-negative integer-valued random variables and {Xn;n≥1} are independent non-negative random variables with distribution, Fn, of Xn, independent of {N(t); t≥0}. Special attention is paid to the distribution of dominated variation. 相似文献
4.
Kong Fanchao Zhang Ying 《高校应用数学学报(英文版)》2007,22(1):78-86
In this paper the large deviation results for partial and random sums Sn-ESn=n∑i=1Xi-n∑i=1EXi,n≥1;S(t)-ES(t)=N(t)∑i=1Xi-E(N(t)∑i=1Xi),t≥0are proved, where {N(t); t≥ 0} is a counting process of non-negative integer-valued random variables, and {Xn; n ≥ 1} are a sequence of independent non-negative random variables independent of {N(t); t ≥ 0}. These results extend and improve some known conclusions. 相似文献
5.
关于大偏差概率的一个界 总被引:1,自引:1,他引:0
研究得到了关于随机和S(t)=∑N(t)i=1Xi,t≥0大偏差的幂的一个界,其中(N(t))t≥0是一族非负整值随机变量,(Xn)n∈N是独立同分布的随机变量,其共同的分布函数是F与(N(t))t≥0独立.本结论是在假设分布函数F的右尾属于ERV族的情况下得到的. 相似文献
6.
丁邦俊 《高校应用数学学报(A辑)》1998,13(2):159-166
设X1,X2……Xn为非负随机变量,相互独立具有共同的分布函数F(t),Y1,Y2……Yn是相应的干扰随机变量,非负,相互独立具有共同的分布G(t),并且Xi与Yi也相互独立,文章在仅能观察到Zi=min(Xi,Yi).δi=I(Xi≤Yi),i=1,2……,n和假设G已知的情况下.分别定义了F的均值和方差的估计量,并求出了估计量的近似分布. 相似文献
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设{Xk,i;k≥1,i≥1)是一随机变量组列,令{pn;n≥1)是一正整数序列,满足c1≤n/pn≤c2,其中c1,c2是正实数.假设{Xk,i;k≥1,i≥1}满足一些相依条件,得到了Ln的渐近分布,这里Ln= ,以及表示(X1,i,…,Xn,i)'和(X1,j,…,Xn,j)'间的Pearson相关系数. 相似文献
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A contribution to large deviations for heavy-tailed random sums 总被引:22,自引:0,他引:22
In this paper we consider the large deviations for random sums
, whereX
n,n⩾1 are independent, identically distributed and non-negative random variables with a common heavy-tailed distribution function
F, andN(t), t⩾0 is a process of non-negative integer-valued random variables, independent ofX
n,n⩾1. Under the assumption that the tail of F is of Pareto’s type (regularly or extended regularly varying), we investigate what
reasonable condition can be given onN(t), t⩾0 under which precise large deviation for S( t) holds. In particular, the condition we obtain is satisfied for renewal counting
processes. 相似文献
12.
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. 相似文献
13.
This paper is a further investigation of large deviation for partial and random sums of random variables, where {Xn,n ≥ 1} is non-negative independent identically distributed random variables with a common heavy-tailed distribution function F on the real line R and finite mean μ∈ R. {N(n),n ≥ 0} is a binomial process with a parameter p ∈ (0,1) and independent of {Xn,n ≥ 1}; {M(n),n ≥ 0} is a Poisson process with intensity λ 〉 0, Sn = ΣNn i=1 Xi-cM(n). Suppose F ∈ C, we futher extend and improve some large deviation results. These results can apply to certain problems in insurance and finance. 相似文献
14.
考虑一类稀疏过程下索赔相依的两险种风险模型:U(t)=u+ct-∑i=1N2(t)X_i-∑i=1N2(t)Y_(i),其中{N_1(t),t≥0}、{N_2(t),t≥0}分别表示两个险种的索赔次数,它们按下述方式相关:N_1(t)N_(11)(t)+N_(12)(t),N_2(t)=N_(22)(t)+N'_(12)(t),{N'_(12)(t),t≥0}是{N_(12)(t),t≥0}的一个p-稀疏.考虑下列两种情形:(Ⅰ){N_(11)(t),t≥0}、{N_(12)(t),t≥0}、{N_(22)(t),t≥0}均为Poisson过程;(Ⅱ){N_(11)(t),t≥0}、{N_(22)(t),t≥0}为Poisson过程,{N_(12)(t),t≥0}为Erlang(2)过程.在上述两种情形下,当两险种的单次索赔额均服从指数分布时,通过建立并求解生存概率所满足的微分方程,给出其破产概率的表达式. 相似文献
15.
Convergence Rates of Wavelet Estimators in Semiparametric Regression Models Under NA Samples 总被引:1,自引:0,他引:1
Consider the following heteroscedastic semiparametric regression model:yi =XTiβ + g(ti) + σiei, 1 < i ≤ n,where {Xi,1 < i < n} are random design points,errors {ei,1 < i < n} are negatively associated (... 相似文献
16.
独立与NA列部分和的精致渐近性 总被引:8,自引:2,他引:6
令{X,Xi:i≥1)为属于非退化稳定分布一般吸引场的独立同分布随机变量列,Sn=∑i=1nXi.本文对十分广泛的拟权函数和边界函数得到了Sn的精致渐近的结果和正态吸引场强平稳NA列部分和的精致渐近的结果,改进并推广了Wang等的结果,从而使此前关于独立列和NA列部分和精致渐近性方面的许多经典的和最新的结果都可以包括在本文的框架之内. 相似文献