共查询到20条相似文献,搜索用时 9 毫秒
1.
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
2.
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
3.
For the widely orthant dependent (WOD) structure, this paper mainly investigates the precise large deviations for the partial sums ofWOD and non-identically distributed random variables with dominatedly varying tails. The obtained results extend some corresponding results. 相似文献
4.
江涛 《高校应用数学学报(A辑)》2003,18(1):77-80
设{Xκ,κ≥1}为一列独立同分布的非随机变量,且具有共同的分布函数F。记Sn为序列{Xκ,κ≥1}的前n项部分和。在F属于ERV分布族的假定下,文中证明了关于随机和SN(t)的随机中心化的精细大偏差结果。这里N(t)为一个与{Xκ,κ≥1}独立的非负整数值的随机过程。 相似文献
5.
6.
Paul H. Schuette 《Journal of Theoretical Probability》1994,7(1):3-45
Given a sequence of independent, but not necessarily identically distributed random variables,Y
i
, letS
k
denote thekth partial sum. Define a function
by taking
to be the piecewise linear interpolant of the points (k, S
k
), evaluated att, whereS
0=0, andk=0, 1, 2,... Fort[0, 1], let
. The
are called trajectories. With regularity and moment conditions on theY
i
, a large deviation principle is proved for the
. 相似文献
7.
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
8.
In this paper, we obtain sample path and scalar large deviation principles for the product of sums of positive random variables. We study the case when the positive random variables are independent and identically distributed and bounded away from zero or the left tail decays to zero sufficiently fast. The explicit formula for the rate function of a scalar large deviation principle is given in the case when random variables are exponentially distributed. 相似文献
9.
M-negatively associated random variables,which generalizes the classical one of negatively associated random variables and includes m-dependent sequences as its par- ticular case,are introduced and studied.Large deviation principles and moderate devi- ation upper bounds for stationary m-negatively associated random variables are proved. Kolmogorov-type and Marcinkiewicz-type strong laws of large numbers as well as the three series theorem for m-negatively associated random variables are also given. 相似文献
10.
11.
Large deviations of sums of independent random variables 总被引:3,自引:0,他引:3
12.
Leonid Rozovsky 《Statistics & probability letters》2012,82(1):72-76
In the note we study large and superlarge deviation probabilities of sum of i.i.d. lattice random variables, whose distribution function has an exponentially decreasing tail at infinity. 相似文献
13.
14.
Let X
1
, X
2
, . . . be a sequence of negatively dependent and identically distributed random variables, and let N be a counting random variable independent of X
i
’s. In this paper, we study the asymptotics for the tail probability of the random sum SN = ?k = 1N Xk {S_N} = \sum\nolimits_{k = 1}^N {{X_k}} in the presence of heavy tails. We consider the following three cases: (i) P(N > x) = o(P(X
1
> x)), and the distribution function (d.f.) of X
1 is dominatedly varying; (ii) P(X
1
> x) = o(P(N > x)), and the d.f. of N is dominatedly varying; (iii) the tails of X
1 and N are asymptotically comparable and dominatedly varying. 相似文献
15.
We prove a large deviation principle for Minkowski sums of i.i.d. random compact sets in a Banach space, that is, the analog of Cramér theorem for random compact sets.
16.
Lithuanian Mathematical Journal - In this paper, we investigate the large deviations of sums of weighted random variables that are approximately independent, generalizing and improving some results... 相似文献
17.
Xue-min Ma 《应用数学学报(英文版)》2011,27(2):209-222
In this paper,we propose a customer-based individual risk model,in which potential claims by customers are described as i.i.d.heavy-tailed random variables,but different insurance policy holders are allowed to have different probabilities to make actual claims.Some precise large deviation results for the prospective-loss process are derived under certain mild assumptions,with emphasis on the case of heavy-tailed distribution function class ERV(extended regular variation).Lundberg type limiting results on the finite time ruin probabilities are also investigated. 相似文献
18.
MIAO Yu & MU JianYong College of Mathematics Information Science Henan Normal University Xinxiang China 《中国科学 数学(英文版)》2011,(4)
Let(Xn)n≥1 be a sequence of independent identically distributed(i.i.d.) positive random variables with EX1 = μ,Var(X1) = σ2.In the present paper,we establish the moderate deviations principle for the products of partial sums(Πnk=1Sk/n!μn)1/(γbn√(2n))1where γ = σ/μ denotes the coefficient of variation and(bn) is the moderate deviations scale. 相似文献
19.
Superlarge deviations for sums of random variables with arithmetical super-exponential distributions
Local limit theorems are obtained for superlarge deviations of sums S(n) = ξ(1) + ... + ξ(n) of independent identically distributed random variables having an arithmetical distribution with the right-hand tail decreasing faster that that of a Gaussian law. The distribution of ξ has the form ?(ξ = k) = \(e^{ - k^\beta L(k)} \), where β > 2, k ∈ ? (? is the set of all integers), and L(t) is a slowly varying function as t → ∞ which satisfies some regularity conditions. These theorems describing an asymptotic behavior of the probabilities ?(S(n) = k) as k/n → ∞, complement the results on superlarge deviations in [4, 5]. 相似文献
20.
GAO Fuqing School of Mathematics Statistics Wuhan University Wuhan China 《中国科学A辑(英文版)》2006,49(12):1753-1767
We first give a functional moderate deviation principle for random processes with stationary and independent increments under the Ledoux's condition. Then we apply the result to the functional limits for increments of the processes and obtain some Csorgo-Revesz type functional laws of the iterated logarithm. 相似文献