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1.
M. N. Feller 《Ukrainian Mathematical Journal》1992,44(3):362-367
We obtain optimal (in a certain sense) harmonicity conditions on functions on a Hilbert space which follow from estimates for sums of independent random variables. Together with the harmonicity conditions obtained earlier, based on estimates of the order of growth for sums of dependent random variables and for sums of orthogonal random variables, they make it possible to consider new classes of harmonic functions of an infinite number of variables.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 3, pp. 417–423, March, 1992. 相似文献
2.
M. N. Feller 《Ukrainian Mathematical Journal》1990,42(11):1419-1423
The infinite-dimensional Laplacian (introduced by P. Levy in 1922) has a number of unusual properties. In particular, the supply of harmonic functions of an infinite number of variables connected with this Laplacian is exceptionally large. In this paper, with the help of estimates of the growth of sums of dependent random variables we get (in a certain sense) optimal conditions for functions on a Hilbert space to be harmonic.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 11, pp. 1576–1579, November, 1990. 相似文献
3.
Eugenijus Manstavi?ius 《Discrete Mathematics》2011,311(6):463
We deal with the random combinatorial structures called assemblies. Instead of the traditional logarithmic condition which assures asymptotic regularity of the number of components of a given order, we assume only lower and upper bounds of this number. Using the author’s analytic approach, we generalize the independent process approximation in the total variation distance of the component structure of an assembly. To evaluate the influence of strongly dependent large components, we obtain estimates of the appropriate conditional probabilities by unconditioned ones. The estimates are applied to examine additive functions defined on a new class of structures, called weakly logarithmic. Some analogs of Major’s and Feller’s theorems which concern almost sure behavior of sums of independent random variables are proved. 相似文献
4.
V. V. Petrov 《Journal of Mathematical Sciences》1981,16(2):994-996
Some estimates are proved for sums of dependent random variables. Theorem 1 contains no assumptions regarding the existence of moments of the random variables. In Theorem 2 estimates are given for the growth of sums of random variables in a stationary sequence.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akad. Nauk SSSR, Vol. 55, pp. 113–116, 1976. 相似文献
5.
We establish strong invariance principles for sums of stationary ??-mixing random variables with finite and infinite second moments under weaker mixing rates. Some earlier results are improved. As applications, some results of the law of the iterated logarithm with finite and infinite variance are obtained, also a conjecture raised by Shao in 1993 is solved. 相似文献
6.
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
7.
8.
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
9.
V. V. Petrov 《Vestnik St. Petersburg University: Mathematics》2016,49(4):371-372
General results on the applicability of the strong law of large numbers to a sequence of dependent random variables, as formulated in terms of estimates for the moments of sums of such variables, are applied to give new conditions of the applicability of this law to (in a wide sense) a stationary sequence of random variables. 相似文献
10.
The paper concerns the study of new classes of parametric optimization problems of the so-called infinite programming that are generally defined on infinite-dimensional spaces of decision variables and contain, among other constraints, infinitely many inequality constraints. These problems reduce to semi-infinite programs in the case of finite-dimensional spaces of decision variables. We focus on DC infinite programs with objectives given as the difference of convex functions subject to convex inequality constraints. The main results establish efficient upper estimates of certain subdifferentials
of (intrinsically nonsmooth) value functions in DC infinite programs based on advanced tools of variational analysis and generalized differentiation. The value/marginal
functions and their subdifferential estimates play a crucial role in many aspects of parametric optimization including well-posedness and sensitivity. In this paper we apply the obtained subdifferential estimates to establishing verifiable conditions for the local Lipschitz continuity of the value functions and deriving necessary optimality conditions in parametric DC infinite programs and their remarkable specifications. Finally, we employ the value function approach and
the established subdifferential estimates to the study of bilevel finite and infinite programs with convex data on both lower and upper level of hierarchical optimization. The results obtained
in the paper are new not only for the classes of infinite programs under consideration but also for their semi-infinite counterparts. 相似文献
11.
LIN ZhengYan & ZHAO YueXu 《中国科学 数学(英文版)》2012,(10):2156-2179
We establish strong invariance principles for sums of stationary ρ-mixing random variables with finite and infinite second moments under weaker mixing rates.Some earlier results are improved.As applications,some results of the law of the iterated logarithm with finite and infinite variance are obtained,also a conjecture raised by Shao in 1993 is solved. 相似文献
12.
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
13.
Complete Convergence and Complete Moment Convergence for Maximal Weighted Sums of Extended Negatively Dependent Random Variables
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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
14.
V. V. Petrov 《Journal of Mathematical Sciences》2006,133(3):1342-1344
Almost sure estimates of the growth of sums of nonnegative random variables are established. A generalization of author's
result on the growth of sums of the indicators of arbitrary events is obtained. Bibliography: 10 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 311, 2004, pp. 237–241. 相似文献
15.
利用王岳宝等将乘积和转化为部分和的乘积之和的方法,研究了随机变量序列乘积和的矩完全收敛性,获得了乘积和矩完全收敛的充分条件. 相似文献
16.
We investigate random variables in Lorentz spaces Lp,q. Conditionson the characteristic function are obtained which imply thata random variable belongs to the Lorentz space. Using them,we prove some estimates for the Lp,q-norm of sums of independentrandom variables. Some of these estimates are new for the spacesLp. 相似文献
17.
A. I. Sakhanenko 《Siberian Mathematical Journal》2011,52(4):696-710
We obtain estimates for the accuracy with which a random broken line constructed from sums of independent nonidentically distributed
random variables can be approximated by a Wiener process. All estimates depend explicitly on the moments of the random variables;
meanwhile, these moments can be of a rather general form. In the case of identically distributed random variables we succeed
for the first time in constructing an estimate depending explicitly on the common distribution of the summands and directly
implying all results of the famous articles by Komlós, Major, and Tusnády which are devoted to estimates in the invariance
principle. 相似文献
18.
Negatively associated (NA) random variables are a more general class of random variables which include a set of independent random variables and have been applied to many practical fields. In this paper, the complete moment convergence of weighted sums for arrays of row-wise NA random variables is investigated. Some sufficient conditions for complete moment convergence of weighted sums for arrays of row-wise NA random variables are established. Moreover, under the weaker conditions, we extend the results of Baek et al. [J. Korean Stat. Soc. 37 (2008), pp. 73–80] and Sung [Abstr. Appl. Anal. 2011 (2011)]. As an application, the complete moment convergence of moving average processes based on an NA random sequence is obtained, which improves the result of Li and Zhang [Stat. Probab. Lett. 70 (2004), pp. 191–197 ]. 相似文献
19.
A. D. Barbour 《Probability Theory and Related Fields》1986,72(2):289-303
Summary Stein's method is used to derive asymptotic expansions for expectations of smooth functions of sums of independent random variables, together with Lyapounov estimates of the error in the approximation. 相似文献
20.
Summary For sums of finite range potential functions of an iid random field we derive the validity of formal expansions of length two. Under standard conditions, formal expansions are valid if and only if the characteristic functions of the sum converge to zero for all nonzero frequency parameters. If this convergence fails, the distribution of the sum can be approximated by a mixture of lattice distributions. The result applies to m-dependent random fields generated by independent random variables. 相似文献