共查询到20条相似文献,搜索用时 796 毫秒
1.
Makoto Maejima 《Journal of Theoretical Probability》1993,6(1):57-69
Limit laws for trimmed sums of triangular arrays of i.i.d. Banach space valued random variables are studied. It is shown that if the array belongs to the domain of attraction of an infinitely divisible law without Gaussian component on a separable Banach space of type 2, then the trimmed sum converges weakly to a nondegenerate Banach space valued random variable. 相似文献
2.
Anja Janßen 《Probability Theory and Related Fields》2010,146(3-4):515-533
We study the limit behavior of power sums and norms of i.i.d. positive samples from the max domain of attraction of an extreme value distribution. To this end, we combine limit theorems for sums and for maxima and use a link between extreme value theory and the Lévy measures of certain infinitely divisible laws, which are limit distributions of power sums. In connection with the von Mises representation of the Gumbel max domain of attraction, this new approach allows us to extend the limit results for power sums found in Ben Arous et al. (Probab Theory Relat Fields 132:579–612, 2005) and Bogachev (J Theor Probab 19:849–873, 2006). Furthermore, our findings shed a new light on the results of Schlather (Ann Probab 29:862–881, 2001) and treat the Gumbel case which is missing there. 相似文献
3.
In the paper, the upper bound and lower bound of the law of the single logarithm (LSL) are established under the condition that the sequence of the normalized weighted sums of random elements is bounded in probability. The main result improves the upper bound in [Sung, S.H., 2009. A law of the single logarithm for weighted sums of i.i.d. random elements. Statist. Probab. Lett., 79, 1351–1357] and hence extends the result in [Chen, P., Gan, S., 2007. Limiting behavior of weighted sums of i.i.d. random variables. Statist. Probab. Lett., 77, 1589–1599]. 相似文献
4.
Uwe Einmahl 《Probability Theory and Related Fields》1988,77(1):65-85
Summary We obtain a strong approximation theorem for partial sums of i.i.d.d-dimensional r.v.'s with possibly infinite second moments. Using this result, we can extend Philipp's strong invariance principle for partial sums of i.i.d.B-valued r.v.'s satisfying the central limit theorem toB-valued r.v.'s which are only in the domain of attraction of a Gaussian law. This new strong invariance principle implies a compact as well as a functional law of the iterated logarithm which improve some recent results of Kuelbs (1985). 相似文献
5.
We provide precise bounds for tail probabilities, say {M
n
x}, of sums M
n
of bounded i.i.d. random variables. The bounds are expressed through tail probabilities of sums of i.i.d. Bernoulli random variables. In other words, we show that the tails are sub-Bernoullian. Sub-Bernoullian tails are dominated by Gaussian tails. Possible extensions of the methods are discussed. 相似文献
6.
The aim of this paper is to derive consequences of a result of G?tze and Zaitsev (2008). We show that the i.i.d. case of this result implies a multidimensional version of some results of Sakhanenko (1985). We establish bounds for the rate of strong Gaussian approximation of sums of i.i.d. R
d
-valued random vectors ξ
j
having finite moments E IIξ
j
IIγ, γ>2. Bibliography: 13 titles. 相似文献
7.
8.
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.
9.
We study the upper-lower class behavior of weighted sums ∑
k=1
n
a
k
X
k
, where X
k
are i.i.d. random variables with mean 0 and variance 1. In contrast to Feller’s classical results in the case of bounded
X
j
, we show that the refined LIL behavior of such sums depends not on the growth properties of (a
n
) but on its arithmetical distribution, permitting pathological behavior even for bounded (a
n
). We prove analogous results for weighted sums of stationary martingale difference sequences. These are new even in the unweighted
case and complement the sharp results of Einmahl and Mason obtained in the bounded case. Finally, we prove a general upper-lower
class test for unbounded martingales, improving several earlier results in the literature. 相似文献
10.
A. Yu. Zaitsev 《Journal of Mathematical Sciences》2008,152(6):875-884
The aim of this paper is to derive new optimal bounds for the rate of strong Gaussian approximation of sums of i.i.d. R
d-valued random variables ξj that have finite moments of the form EH (‖ξj‖), where H (x) is a monotone function growing not slower than x2 and not faster than ecx. We obtain some generalization and improvements of results of U. Einmahl (1989). Bibliography: 28 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 351, 2007, pp. 141–158. 相似文献
11.
Andrei N. Frolov 《Acta Appl Math》2003,78(1-3):129-136
The almost sure asymptotic behavior of large increments of partial sums is investigated in case of independent nonidentically distributed random variables. One-sided variants of the Csörg–Révész strong approximation laws are obtained in non-i.i.d. case. 相似文献
12.
Uwe Einmahl 《Probability Theory and Related Fields》1989,82(2):213-223
Summary Kuelbs (1975) established a Kolmogorov-Erdös-Petrowski type integral test for lower and upper classes in the law of the iterated logarithm for sums of i.i.d. Hilbert space valued Gaussian mean zero random variables. We show that this integral test remains valid for sums of i.i.d. pregaussian mean zero random variables satisfying an additional (very mild) assumption. 相似文献
13.
Vladimir Pozdnyakov 《Discrete Applied Mathematics》2008,156(1):93-102
A new martingale technique is developed to find formulas for the expected value and generating function of the waiting time until one observes a gapped pattern (or a structured motif) in an i.i.d. sequence of random letters from a finite alphabet. 相似文献
14.
Lin Zhengyan 《数学年刊B辑(英文版)》1990,11(3):376-383
The Erdos-Renyi law of large numbers (1970) is the first important result forasymptotic behaviours of increments of partial sams of a sequence of random variableswith apan [ClogN]. Some generalizations have been done sinoe then, such as conver-gence rate of the limit, some results when order of span being either higher or lowerthan log N. But all these results are only obtained in the case of i. i. d. random variables.This paper aims at the generalization of these results to the ease when random variablesare independent, but not necessarily identically distributed. To this end Chernoff Theoremis generalized to the corlesponding case at first. 相似文献
15.
In this paper, we study the joint limit distributions of point processes of exceedances and partial sums of multivariate Gaussian sequences and show that the point processes and partial sums are asymptotically independent under some mild conditions. As a result, for a sequence of standardized stationary Gaussian vectors, we obtain that the point process of exceedances formed by the sequence (centered at the sample mean) converges in distribution to a Poisson process and it is asymptotically independent of the partial sums. The asymptotic joint limit distributions of order statistics and partial sums are also investigated under different conditions. 相似文献
16.
We establish a Berry-Esséen bound for Student's statistic for independent (nonidentically) distributed random variables. In particular, the bound implies a sharp estimate similar to the classical Berry-Esséen bound. In the i.i.d. case it yields sufficient conditions for the Central Limit Theorem for studentized sums. For non-i.i.d. random variables the bound shows that the Lindeberg condition is sufficient for the Central Limit Theorem for studentized sums.Research supported by the SFB 343 in Bielefeld. 相似文献
17.
该文研究了NOD序列加权和的强收敛速度, 获得了一些新的完全收敛性的结果. 该文的结果推广了陈瑞林$^{[1]}$在NA情形时的结果,部分推广了Stout$^{[2]}$在独立同分布情形时的结果. 相似文献
18.
19.
Arunava Mukherjea 《Probability Theory and Related Fields》1991,87(3):389-401
Summary In this paper we present a necessary and sufficient condition for tightness of products of i.i.d. finite dimensional random nonnegative matrices. We give an example illustrating the use of our theorem and treat completely the case of 2×2 matrices. We also describe stationary solutions of the linear equationy
n=Xnyn–1, n>0, in (R
d
)+, whereX
1,X
2,... are i.i.d.d×d nonnegative matrices. 相似文献
20.
Qunying WU 《数学年刊B辑(英文版)》2012,33(6):919-930
Consider a sequence of i.i.d. positive random variables with the underlying distribution in the domain of attraction of a stable distribution with an exponent in (1, 2]. A universal result in the almost sure limit theorem for products of partial sums is established. Our results significantly generalize and improve those on the almost sure central limit theory previously obtained by Gonchigdanzan and Rempale and by Gonchigdanzan. In a sense, our results reach the optimal form. 相似文献