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 共查询到20条相似文献,搜索用时 15 毫秒
1.
The object of this research in queueing theory is the Law of the Iterated Logarithm (LIL) under the conditions of heavy traffic in Multiphase Queueing Systems (MQS). In this paper, the LIL is proved for extreme values of important probabilistic characteristics of the MQS investigated as well as maxima and minima of the summary queue length of customers and maxima and minima of the queue length of customers. Also, the paper presents a survey on the works for extreme values in queues and the queues in heavy traffic.   相似文献   

2.
迭代Brown运动的一个Chung型重对数律   总被引:1,自引:0,他引:1  
尹传存  吕玉华 《数学学报》2000,43(1):99-102
X及Y分别为Rd1及Rd2中的相互独立的标准Brown运动,满足X(0)=Y(0)=0.定义,称为一个迭代Brown运动.本文给出了关于Zd1,d2的一个Chung型重对数律.  相似文献   

3.
邓学斌 《数学研究》2000,33(2):153-156
证明了关于独立同分布随机变量序列的加权U-统计量的一个重对数律,类似于献「3」证明了一个加权U-统计量的解耦不等式。  相似文献   

4.
在本文中,我们证明了两参数OU过程的钟重对数律。  相似文献   

5.
陈平炎  黄立虎 《数学学报》2000,43(6):1063-107
设{Xn,n≥ 0}是独立同分布的随机变量序列,其分布函数是一个对称的指数为 a(0< a< 2)的稳定分布·本文证明了依概率 1有 lim supβ-l-|( l-βα)1/α∑∞ n=0βnXn=exp(1/α)·  相似文献   

6.
The objective of this research in the queueing theory is the law of the iterated logarithm (LIL) under the conditions of heavy traffic in multiphase queueing systems (MQS). In this paper, the LIL is proved for the extreme values of some important probabilistic characteristics of the MQS, namely, maxima and minima of the summary waiting time of a customer, and maxima and minima of the waiting time of a customer.  相似文献   

7.
8.
Let \({\widetilde{H}}_N\), \(N \ge 1\), be the point-to-point last passage times of directed percolation on rectangles \([(1,1), ([\gamma N], N)]\) in \({\mathbb {N}}\times {\mathbb {N}}\) over exponential or geometric independent random variables, rescaled to converge to the Tracy–Widom distribution. It is proved that for some \(\alpha _{\sup } >0\),
$$\begin{aligned} \alpha _{\sup } \, \le \, \limsup _{N \rightarrow \infty } \frac{{\widetilde{H}}_N}{(\log \log N)^{2/3}} \, \le \, \Big ( \frac{3}{4} \Big )^{2/3} \end{aligned}$$
with probability one, and that \(\alpha _{\sup } = \big ( \frac{3}{4} \big )^{2/3}\) provided a commonly believed tail bound holds. The result is in contrast with the normalization \((\log N)^{2/3}\) for the largest eigenvalue of a GUE matrix recently put forward by E. Paquette and O. Zeitouni. The proof relies on sharp tail bounds and superadditivity, close to the standard law of the iterated logarithm. A weaker result on the liminf with speed \((\log \log N)^{1/3}\) is also discussed.
  相似文献   

9.
D. Ferger 《Acta Appl Math》2003,78(1-3):115-120
We prove a functional law of the iterated logarithm for U-statistics type processes. The result is used to determine the almost sure set of limit points for change-point estimators.  相似文献   

10.
设{X,Xn;n≥0}是一取值于可分Banach空间中的同分布Φ~*-混合随机变量序列,并记其几何加权级数为ξ(β)=sum from n=0 to ∞β~nX_n,其中0<β<1.在X的二阶矩可能不存在的条件下,建立了ξ(β)的一个广义重对数律.  相似文献   

11.
Let {X,X n ,n≥1} be a sequence of independent identically distributed random variables with EX=0 and assume that EX 2 I(|X|≤x) is slowly varying as x→∞. In this paper it is shown that a Strassen-type law of the iterated logarithm holds for self-normalized sums of such random variables, i.e., when X is in the domain of attraction of the normal law.  相似文献   

12.
陈平炎  柳向东 《数学学报》2003,46(5):999-100
对于具有某种尾渐近行为的独立同分布的随机变量序列,本文通过积分检验刻划了其加权部分和的极限结果,并作为推论获得了Chover型重对数律。把这些结果应用到经典的可和方式,获得了相应的结果。  相似文献   

13.
ρ-混合序列的重对数律   总被引:3,自引:0,他引:3  
蔡光辉 《数学学报》2006,49(1):155-160
设{Xn,n≥1}是同分布ρ-混合序列,其分布属于特征指数为α(0<α<2) 的非退化稳定分布的正则吸引场,证明了依概率1有lira supn→∞ = e1/α,并获得了一系列等价条件.此结果的获得不仅将已有的一些结果推广至ρ-混合序列的情形,并且将其结果作了一定的改进.  相似文献   

14.
15.
Iterated Logarithm Law for Anticipating Stochastic Differential Equations   总被引:1,自引:0,他引:1  
We prove a functional law of iterated logarithm for the following kind of anticipating stochastic differential equations
where u>e, W={(W t 1,…,W t k ),0≤t≤1} is a standard k-dimensional Wiener process, are functions of class with bounded partial derivatives up to order 2, X 0 u is a random vector not necessarily adapted and the first integral is a generalized Stratonovich integral. The work is partially supported by DGES grant BFM2003-01345.  相似文献   

16.
17.
Consider a double array of i.i.d. random variables with mean and variance and set . Let denote the empirical distribution function of Z1, n ,..., Z N, n and let be the standard normal distribution function. The main result establishes a functional law of the iterated logarithm for , where n=n(N) as N. For the proof, some lemmas are derived which may be of independent interest. Some corollaries of the main result are also presented.  相似文献   

18.
We investigate the asymptotic properties of one-dimensional Gaussian autoregressive processes of the second order. We prove the law of the iterated logarithm in the case of an unstable autoregressive model.  相似文献   

19.
给出了非同分布NA列满足对数律和重对数律的一些矩条件,而文[50-[7]中的部分结果可以成为其特殊情形并得到加强.  相似文献   

20.
Laws of the iterated logarithm are established for the local U-statistic process. This entails the development of probability inequalities and moment bounds for U-processes that should be of separate interest. The local U-statistic process is based upon an estimator of the density of a function of several i.i.d. variables proposed by Frees (J. Am. Stat. Assoc. 89, 517–525, 1994). As a consequence, our results are directly applicable to the derivation of exact rates of uniform in bandwidth consistency in the sup and in the L p norms for these estimators. Research of E. Giné partially supported by NSA Grant H98230-04-1-0075. Research of D.M. Mason partially supported by NSA Grant MDA904-02-1-0034 and NSF Grant DMS-0503908.  相似文献   

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