共查询到20条相似文献,搜索用时 15 毫秒
1.
The present paper first shows that, without any dependent structure assumptions for a sequence of random variables, the refined results of the complete convergence for the sequence is equivalent to the corresponding complete moment convergence of the sequence. Then this paper investigates the convergence rates and refined convergence rates (or complete moment convergence) for probabilities of moderate deviations of moving average processes. The results in this paper extend and generalize some well-known results. 相似文献
2.
André Adler 《Journal of Theoretical Probability》2002,15(4):939-949
Consider independent and identically distributed random variables {X,X
nj
, 1jn,n1} with density f(x)=px
–p–1
I(x1), where p>0. We show that there exist unusual generalized Laws of the Iterated Logarithm involving the larger order statistics from our array. 相似文献
3.
Let X,X
n
;n1 be a sequence of real-valued i.i.d. random variables with E(X)=0. Assume B(u) is positive, strictly increasing and regularly-varying at infinity with index 1/2<1. Set b
n
=B(n),n1. If
and
for some [0,), then it is shown that
and
for every real triangular array (a
n,k
;1kn,n1) and every array of bounded real-valued i.i.d. random variables W,W
n,k
;1kn,n1`` independent of {X,X
n
;n1}, where (W)=(E(W–E(W))2)1/2. An analogous law of the iterated logarithm for the unweighted sums
n
k=1
X
k
;n1} is also given, along with some illustrative examples. 相似文献
4.
5.
We study complete convergence of martingale arrays under rather weak conditions. Our results considerably strengthen many of the results available in the literature. As a tool, we establish a martingale analogue of an inequality of Hoffman-Jørgensen which was earlier known only for independent random variables. 相似文献
6.
Pingyan Chen 《随机分析与应用》2013,31(1):89-103
Abstract This article considers the partial sums from a sequence of independent and identically distributed random variables. It is well-known that the Hartman-Wintner law of the iterated logarithm holds if and only if the second moment exists. This article studies the generalized law of the iterated logarithm for the partial sums when they are normalized by a sequence of constants that are regularly varying with index 1/2. As a result, two equivalent conditions for the law are obtained. 相似文献
7.
8.
In this paper,we extend the Kolmogorov-type inequality to the case of ψ-mixing sequences.Moreover,we study the strong limit theorems for partial sums of ψ-mixing random variables.As a result,we extend the Khintchine-Kolmogorov-type convergence theorem,the three series theorem,Marcinkiewicz strong law of large number to the case of ψ-mixing sequences. 相似文献
9.
André Adler 《Journal of Theoretical Probability》1992,5(4):707-726
Let {X,X
n,nZ
+
d
} be a sequence of independent and identically distributed random variables and {a
n
,n Z
+
d
} be a sequence of constants. We examine the almost sure limiting behavior of weighted partial sums of the form |n|N
a
n
X
n
. Suppose further that eitherEX=0 orE|X|=. In most situations these normalized partial sums fail to have a limit, no matter which normalizing sequence we choose. Thus, the investigation lends itself to the study of the limit inferior and limit superior of these sequences. On the way to proving results of this type we first establish several weak laws. These weak laws prove to be of great value in establishing generalized laws of the iterated logarithm. 相似文献
10.
Bing-Yi Jing Qi-Man Shao Wang Zhou 《Transactions of the American Mathematical Society》2008,360(8):4263-4285
This paper is an attempt to establish a universal moderate deviation for self-normalized sums of independent and identically distributed random variables without any moment condition. The exponent term in the moderate deviation is specified when the distribution is in the centered Feller class. An application to the law of the iterated logarithm is given.
11.
证明了强平稳正相协列乘积和的重对数律与不同分布正相协列乘积和的强大数律,指出了部分和服从强大数律但乘积和未必服从强大数律这一事实,并讨论了定理2中一个条件的必要性. 相似文献
12.
Xia Chen 《Journal of Theoretical Probability》2006,19(3):721-739
We establish moderate and small deviations for the ranges of integer valued random walks. Our theorems apply to the limsup
and the liminf laws of the iterated logarithm.
We establish moderate and small deviations for the ranges of integer valued random walks. Our theorems apply to the limsup
and the liminf laws of the iterated logarithm. 相似文献
13.
本文讨论了可交换随机变量序列{Xn:n≥1)重对数律的收敛速度,得到了可交换随机变量序列与独立序列类似的极限性质,同时给出了可交换序列重对数律收敛速度的一种描述. 相似文献
14.
邱德华 《数学的实践与认识》2009,39(9)
利用Rosenthal型最大值不等式,得到了NA随机变量加权和的Marcinkiewicz-Zygmund强大数定律和完全收敛性,所获结果推广和改进了一些文献中相应的结果. 相似文献
15.
The results of this paper concern rates of convergence for increments of Brownian motion. As a by-product we give some improvements of a result of Bolthausen dealing with Strassen's law of the iterated logarithm. 相似文献
16.
假设{X_n,n≥1}为一列严平稳的NA随机变量,期望为零,方差有限.设S_n=∑_(i=1)~n∑X_i,M_n=max_(1≤i≤n)|S_i|.在适当的条件下,得到了一类NA序列部分和部分和最大值重对数矩收敛的精确渐近性. 相似文献
17.
Zhonggen Su 《Journal of Theoretical Probability》1996,9(3):679-701
Suppose thatB is a separable Banach space and (S,l,P) a probability space.H is a measurable symmetric kernel function fromS
m
intoB. In this paper we shall further study some limit theorems forB-valuedU-statisticsU
m
n
H based onP andH. Special attention is paid upon the Marcinkiewicz type law of large numbers and the law of the iterated logarithm. Our results can be regarded as extensions of corresponding results for sums of independentB-valued random variables toU-statistics.Research supported by National Natural Science Foundation of China and Zhejiang Province. 相似文献
18.
研究一个每个节点具有多服务台的Jackson网络.在服务强度为1的条件下,研究了Jackson网络的泛函重对数率与其流体逼近的收敛速度,证明了如果该网络的外部到达过程,服务过程有泛函重对数率,且在流体变换下以指数速度收敛到其相应的流体模型,则其队长过程、负荷过程、忙期过程等也具有相应的性质. 相似文献
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