共查询到20条相似文献,搜索用时 46 毫秒
1.
M. A. Lifshits 《Journal of Mathematical Sciences》2002,109(6):2166-2178
We establish a sufficient condition for an almost sure limit theorem for sums of independent random vectors under minimal moment conditions and assumptions on normalizing sequences. We provide an example showing that our condition is close to the optimal one, as well as a related sufficient condition due to Berkes and Dehling. Bibliography: 5 titles. 相似文献
2.
NA序列部分和的矩完全收敛性 总被引:4,自引:0,他引:4
讨论了NA序列部分和的矩完全收敛性,在一定条件下获得了NA序列矩完全收敛的充要条件,显示了矩完全收敛和矩条件之间的关系,将独立同分布随机变量序列矩完全收敛的结果推广到NA序列,得到了与独立随机变量序列情形类似的结果. 相似文献
3.
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
4.
关于随机变量加权和的强收敛性注记 总被引:2,自引:0,他引:2
蔡宗武 《高校应用数学学报(A辑)》1991,6(1):44-51
设{X,;n≥1}为独立同分布随机序列,{a_(xi);1≤i≤K_n,↑~∞,n≥1}为权系数序列。本文给出三组sum from i=1 to K_n(a_(ai)X_i→0a.s.充分条件。同时,还讨论加权和的完全收敛性,我们的条件比[3]弱。 相似文献
5.
Zbigniew S. Szewczak 《Statistics & probability letters》2010,80(9-10):747-751
Residues of partial sums in a class of dependent random variables, including functionals of uniformly recurrent Markov chains, are in the domain of attraction of the uniform distribution. These types of limit theorems arise for example in the multiplication of floating-point numbers. 相似文献
6.
M. A. Lifshits Ya. Yu. Nikitin V. V. Petrov A. Yu. Zaitsev A. A. Zinger 《Vestnik St. Petersburg University: Mathematics》2018,51(2):144-163
This is the first in a series of reviews devoted to the scientific achievements of the Leningrad–St. Petersburg school of probability and statistics in the period from 1947 to 2017. It is devoted to limit theorems for sums of independent random variables—a traditional subject for St. Petersburg. It refers to the classical limit theorems: the law of large numbers, the central limit theorem, and the law of the iterated logarithm, as well as important relevant problems formulated in the second half of the twentieth century. The latter include the approximation of the distributions of sums of independent variables by infinitely divisible distributions, estimation of the accuracy of strong Gaussian approximation of such sums, and the limit theorems on the weak almost sure convergence of empirical measures generated by sequences of sums of independent random variables and vectors. 相似文献
7.
Anscombe (1952) (also see Chung (1974)) has developed a central limit theoremof random sums of independent and identically distributed random variables. Applicability of this theorem in practice, however, is limited since the normalization requires random factors. In this paper we establish sufficient conditions under which the central limit theorem holds when such random factors are replaced by the underlying asymptotic mean and standard ddeviation. An application of this result in the context of shock models is also given. 相似文献
8.
利用m值随机变量的特征函数,在一定条件下,得到了相互独立的m值随机变量和的极限分布均匀的充要条件;再结合无穷乘积的有关性质,给出了相互独立的m值随机变量和极限分布均匀分布的充分条件,特别当m为素数P时,所得的充分条件易于验证,且不难满足。 相似文献
9.
In this paper, the authors discuss the moment
complete convergence for weighted sums of -mixing random
variables, and obtains the sufficient condition for moment complete
convergence of -mixing sequence under some mixing rate
condition, which generalize the result of moment complete
convergence for weighted sums of i.i.d. random variables to
-mixing random variables. 相似文献
10.
Peter Hall 《Probability Theory and Related Fields》1978,44(3):253-260
Summary An early extension of the Lindeberg-Feller Theorem was Bernstein's discovery of necessary and sufficient conditions for the convergence of moments in the central limit theorem for sums of independent random variables. In this paper we show that Bernstein's work has a generalisation to martingales. We extend his work in both the independence and the martingale cases by showing that there exists a duality between the behaviour of the moments of the martingale and the behaviour of the sums of squares of the martingale differences. Our proofs are quite unrelated to Bernstein's and are based on Burkholder's inequalities. 相似文献
11.
N. N. Amosova 《Journal of Mathematical Sciences》2003,118(6):5507-5512
We investigate necessary and sufficient conditions under which one estimate of exponential type is valid for large deviation probabilities of sums of independent identically distributed random variables. Bibliography: 3 titles. 相似文献
12.
We prove limit theorems for row sums of a rowwise independent infinitesimal array of random variables with values in a locally compact Abelian group. First we give a proof of Gaiser's theorem [4, Satz 1.3.6], since it does not have an easy access and it is not complete. This theorem gives sufficient conditions for convergence of the row sums, but the limit measure cannot have a nondegenerate idempotent factor. Then we prove necessary and sufficient conditions for convergence of the row sums, where the limit measure can be also a nondegenerate Haar measure on a compact subgroup. Finally, we investigate special cases: the torus group, the group of p ‐adic integers and the p ‐adic solenoid. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
13.
A. I. Chernyak 《Ukrainian Mathematical Journal》1990,42(5):634-637
We prove a limit theorem on the convergence of nonhomogeneous centered processes of step sums, constructed on random mixing sequences, to a process with independent increments. We also prove a invariance-principle type theorem for schemes of summation of functionals on random mixing sequences.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 5, pp. 716–721, May, 1990. 相似文献
14.
兰冲锋 《数学年刊A辑(中文版)》2015,36(4):401-410
在非同分布的情况下,给出了行为ND随机变量阵列加权和的完全收敛性的充分条件,所得结果部分地推广了独立随机变量和NA随机变量的相应结果.作为其应用,获得了ND随机变量序列加权和的Marcinkiewicz-Zygmund型强大数定律. 相似文献
15.
V. V. Petrov 《Journal of Mathematical Sciences》1983,23(3):2294-2296
A generalization of one theorem of K. Tandori is proved. A sufficient condition is derived for application of a strong law of large numbers to a sequence of orthogonal random variables, expressed in terms of the growth of sums of second moments of these variables. 相似文献
16.
A. N. Chuprunov 《Journal of Mathematical Sciences》1995,76(1):2110-2117
The paper deals with sums of independent and identically distributed random variables defined on some probability space which
are multiplied by random coefficients. These coefficients are the values of independent random variables defined on another
probability space. We obtain conditions for the weak convergence of weighted sums, for almost all coefficients, to some infinitely
divisible distribution. The limit distribution for these sums is found.
Supported by the Russian Foundation for Fundamental Research (grant No. 93-011-16099).
Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, 1993. 相似文献
17.
Ji Gao Yan 《数学学报(英文版)》2018,34(10):1501-1516
In this paper,the complete convergence and complete moment convergence for maximal weighted sums of extended negatively dependent random variables are investigated.Some sufficient conditions for the convergence are provided.In addition,the Marcinkiewicz–Zygmund type strong law of large numbers for weighted sums of extended negatively dependent random variables is obtained.The results obtained in the article extend the corresponding ones for independent random variables and some dependent random variables. 相似文献
18.
A. N. Chuprunov 《Journal of Mathematical Sciences》1997,83(3):381-392
We deal with independent random variables which are the values of a stochastic process taken at random points in time. So
we have random variables depending upon a random parameter. We obtain the conditions providing the weak convergence of random
lines defined by sums or maxima or bilinear forms of these random variables for almost all values of the parameter, to one
and the same stochastic process. These limit stochastic processes are described.
Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russia, 1995, Part II. 相似文献
19.
Operator self-similar processes, as an extension of self-similar processes, have been studied extensively. In this work, we study limit theorems for functionals of Gaussian vectors. Under some conditions, we determine that the limit of partial sums of functionals of a stationary Gaussian sequence of random vectors is an operator self-similar process. 相似文献
20.
Mark Finkelstein Victor M. Kruglov Howard G. Tucker 《Journal of Theoretical Probability》1994,7(3):565-598
We extend results obtained in Kruglov,(7) and Finkelstein and Tucker(3) to obtain necessary and sufficient conditions for convergence in law of random sums of non-identically distributed independent random variables under non-random centering. Thei.i.d. case is also considered for random variables attracted to a stable law. Necessary and sufficient conditions for convergence in law of these random variables under non-random centering, and in some cases, under non-random norming, are also obtained. The distribution functions for the limit laws are determined as well, generalizing results of Robbins.(10)
Supported in part by The State University of New York and United States Information Agency Grant No. IA AEMP69193692. 相似文献