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1.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 194, pp. 124–133, 1992. 相似文献
2.
New sufficient conditions for the applicability of the strong law of large numbers are established for sequences of random
variables without the independence conditions. Results on strong stability of sums of dependent random variables are also
obtained. No particular type of dependence between random variables of a sequence is assumed. Only conditions related to moments
of random variables and their sums are used. It is shown that the results obtained are unimprovable in certain sense. These
results are generalizations of some results of N. Etemadi proved under more restrictive conditions. 相似文献
3.
Pawel Hitczenko 《Probability Theory and Related Fields》1988,78(2):223-230
Summary It is shown that for all tangent sequences (d
n) and (e
n) of nonnegative or conditionally symmetric random variables and for every function satisfying the growth condition (2x)(x) the following inequality holds:
. This generalizes results of J. Zinn and proves a conjecture of S. Kwapie and W.A. Woyczyski. 相似文献
4.
V. B. Nevzorov 《Vestnik St. Petersburg University: Mathematics》2012,45(4):164-167
The scheme of n series of independent random variables X 11, X 21, …, X k1, X 12, X 22, …, X k2, …, X 1n , X 2n , …, X kn is considered. Each of these successive series X 1m , X 2m , …, X km , m = 1, 2, …, n consists of k variables with continuous distribution functions F 1, F 2, …, F k , which are the same for all series. Let N(nk) be the number of upper records of the given nk random variables, and EN(nk) be the corresponding expected value. For EN(nk) exact upper and lower estimates are obtained. Examples are given of the sets of distribution functions for which these estimates are attained. 相似文献
5.
V. M. Korchevsky 《Vestnik St. Petersburg University: Mathematics》2011,44(4):268-271
New sufficient conditions for the applicability of the strong law of large numbers to a sequence of dependent random variables
X
1, X
2, …, with finite variances are established. No particular type of dependence between the random variables in the sequence
is assumed. The statement of the theorem involves the classical condition Σ
n
∞ (log2
n)2/n
2 < ∞, which appears in various theorems on the strong law of large numbers for sequences of random variables without the independence
condition. 相似文献
6.
7.
8.
The aim of the paper is to establish strong laws of large numbers for sequences of blockwise and pairwise m-dependent random variables in a convex combination space with or without compactly uniformly integrable condition. Some of our results are even new in the case of real random variables. 相似文献
9.
10.
V. M. Korchevsky 《Vestnik St. Petersburg University: Mathematics》2010,43(4):217-219
We investigate relationship between Kolmogorov–s condition and Petrov–s condition in theorems on the strong law of large numbers
for a sequence of independent random variables X
1, X
2, … with finite variances. The convergence (S
n
− ES
n
)/n → 0 holds a.s. (here, S
n
= Σ
k=1
n
X
k
), provided that Σ
n=1∞
DX
n
/n
2 < ∞ (Kolmogorov’s condition) or DS
n
= O(n
2/ψ(n)) for some positive non-decreasing function ψ(n) such that Σ1/(nψ(n)) < ∞ (Petrov’s condition). Kolmogorov’s condition is shown to follow from Petrov’s condition. Besides, under some additional
restrictions, Petrov’s condition, in turn, follows from Kolmogorov’s condition. 相似文献
11.
12.
Yehoram Gordon Alexander Litvak Carsten Schütt Elisabeth Werner 《Comptes Rendus Mathematique》2005,340(6):445-448
For a given sequence of real numbers we denote the k-th smallest one by . We show that there exist two absolute positive constants c and C such that for every sequence of positive real numbers and every one has where , , are independent Gaussian random variables. Moreover, if then the left hand side estimate does not require independence of the s. Similar estimates hold for as well. To cite this article: Y. Gordon et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005). 相似文献
13.
John Panaretos 《Annals of the Institute of Statistical Mathematics》1981,33(1):191-198
Summary LetX, Y be two discrete random variables with finite support andX≧Y. Suppose that the conditional distribution ofY givenX can be factorized in a certain way. This paper provides a method of deriving the unique form of the marginal distribution
ofX (and hence the joint distribution of (X, Y)) when partial independence only is assumed forY andX−Y. 相似文献
14.
15.
16.
Dr. P. J. Holewijn 《Probability Theory and Related Fields》1969,14(2):89-92
Summary This paper deals with the almost sure uniform distribution (modulo 1) of sequences of random variables. In the case where the law of the increments X
n+h
–X
n
of the sequence X
0, X
1, does not depend on n, sufficient conditions are given to assure the uniform distribution (modulo 1) with probability one. As an illustrative example the partial sums of a sequence of independent, identically distributed variables is considered. 相似文献
17.
Wolfgang Stadje 《Mathematische Nachrichten》2005,278(10):1209-1229
We consider several aspects of the relationship between a [0, 1]‐valued random variable X and the random sequence of digits given by its m‐ary expansion. We present results for three cases: (a) independent and identically distributed digit sequences; (b) random variables X with smooth densities; (c) stationary digit sequences. In the case of i.i.d. an integral limit thorem is proved which applies for example to relative frequencies, yielding asymptotic moment identities. We deal with occurrence probabilities of digit groups in the case that X has an analytic Lebesgue density. In the case of stationary digits we determine the distribution of X in terms of their transition functions. We study an associated [0, 1]‐valued Markov chain, in particular its ergodicity, and give conditions for the existence of stationary digit sequences with prespecified transition functions. It is shown that all probability measures induced on [0, 1] by such sequences are purely singular except for the uniform distribution. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
18.
Lin Zhengyan 《数学学报(英文版)》1989,5(2):185-192
Consider the weighted sums
of a sequence {X
n} of independent random variables or random elements inD [0,1]. For convergence ofS
n in probability and with probability one, in [2],[3] etc., the following stronger condition is required: {X
n} is uniformly bounded by a random variableX,i.e.P(¦X
n¦x)P(¦X¦x) for allx>0. Our paper aims at trying to drop this restriction.The Project supported by National Natural Science Foundation of China 相似文献
19.
Nasrollah Etemadi 《Journal of multivariate analysis》1983,13(1):187-193
Strong laws of large numbers concerning nonnegative random variables are obtained and then they are utilized to establish stability results, among other things, for sums of pairwise independent random variables and the range of random walks. 相似文献
20.
L. J. Savelyev 《Numerical Analysis and Applications》2013,6(3):221-228
A problem of finding discrete random values and vectors with discrete distributions having a given average value and a minimum dispersion is solved. The vector model is associated with statistical methods of calculating multiple integrals and solving systems of integral equations. 相似文献