共查询到20条相似文献,搜索用时 31 毫秒
1.
A. N. Chuprunov 《Lithuanian Mathematical Journal》1995,35(1):42-52
The paper deals with maxima and sums of independent random variables. These random variables are the values of independent
identically distributed stochastic processes at a random point in time. We obtain conditions for their weak convergence, at
almost all points in time to the same infinitely divisible distribution and describe the limit distribution for these sums.
Some applications of these results to statistics are considered.
This work was supported by the Russian Foundation for Fundamental Research (grant No. 93-011-16099).
Research Institute of Mathematics and Mechanics, Kazan State University, 17 Universitetskaya St., Kazan, 420008, Russia. Translated
from Lietuvos Matematikos Rinkinys, Vol. 5, No. 1, pp. 52–64, January–March, 1995.
Translated by A. N. Chuprunov 相似文献
2.
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
3.
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
4.
L. P. Terekhova 《Lithuanian Mathematical Journal》2009,49(3):318-330
In this paper, we obtain an almost sure functional limit theorem for random sums of multiindex random variables. 相似文献
5.
In this paper we obtain an almost sure version of a limit theorem for random sums of multiindex random variables that belong to the domain of attraction of a p-stable law. 相似文献
6.
The paper deals with random step-line processes defined by sums of independent identically distributed random variables multiplied
by independent indicators. These processes describe some models in which random variables are replaced with other ones. We
prove the convergence in distribution of such processes to the weighted Ornstein-Uhlenbeck process.
Supported by the Hungarian Foundation for Scientific Research (grant No. OTKA-T016933-1996) and by the Hungarian Ministry
of Culture and Education (grant No. 179-1995).
Proceedings of the Seminar on Stability Problems for Stochastic Models, Hajdúszoboszló, Hungary, 1997, Part I. 相似文献
7.
B. Meredov 《Ukrainian Mathematical Journal》1991,43(1):117-121
There are proved limit theorems for random processes constructed from sums of independent identically distributed random variables.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 1, pp. 141–145, January, 1991. 相似文献
8.
Z. A. Enikeeva 《Lithuanian Mathematical Journal》2005,45(1):24-33
We obtain a limit theorem of convergence in distribution for random polygonal lines defined by sums of independent random variables with replacements. In a particular case, the limit is the Gaussian Ornstein-Uhlenbeck process.__________Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 1, pp. 33–44, January–March, 2005.Translated by V. Mackeviius 相似文献
9.
William N. Hudson Howard G. Tucker Jerry A. Veeh 《Probability Theory and Related Fields》1989,82(1):9-17
Summary The set of limit distributions of row sums of a triangular array of Bernoulli random variables which is strictly stationary and m-dependent in each row is characterized. Necessary and sufficient conditions for the convergence of the row sums to a given limit distribution are found. The case of convergence to a Poisson distribution is given special attention. 相似文献
10.
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
11.
Summary Moment inqualities and strong laws of large numbers are proved for random allocations of balls into boxes. Random broken lines
and random step lines are constructed using partial sums of i.i.d. random variables that are modified by random allocations.
Functional limit theorems for such random processes are obtained. 相似文献
12.
胡宏昌 《纯粹数学与应用数学》2014,(6):558-563
为了完善 AANA 序列的极限理论,利用三级数定理、Borel-Cantelli 引理及一些概率不等式,研究了AANA 随机变量序列的函数加权和。在一定的条件下,得到了其一致强收敛速度为n?13 log n,推广了关于NA随机变量序列的相应结果。 相似文献
13.
In this paper, we obtain an almost sure central limit theorem for products of independent sums of positive random variables. An extension of the result gives an ASCLT for the U-statistics. 相似文献
14.
Romuald Lenczewski 《Journal of Functional Analysis》2010,258(12):4075-1844
We show that the framework developed by Voiculescu for free random variables can be extended to arrays of random variables whose multiplication imitates matricial multiplication. The associated notion of independence, called matricial freeness, can be viewed as a concept which not only leads to a natural generalization of freeness, but also underlies other fundamental types of noncommutative independence, such as monotone independence and boolean independence. At the same time, the sums of matricially free random variables, called random pseudomatrices, are closely related to random matrices. The main results presented in this paper concern the standard and tracial central limit theorems for random pseudomatrices and the corresponding limit distributions which can be viewed as matricial semicircle laws. 相似文献
15.
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
16.
Zhong Gen Su 《数学学报(英文版)》2008,24(6):971-982
The author considers the largest eigenvaiues of random matrices from Gaussian unitary ensemble and Laguerre unitary ensemble, and the rightmost charge in certain random growth models. We obtain some precise asymptotics results, which are in a sense similar to the precise asymptotics for sums of independent random variables in the context of the law of large numbers and complete convergence. Our proofs depend heavily upon the upper and lower tail estimates for random matrices and random growth models. The Tracy-Widom distribution plays a central role as well. 相似文献
17.
W. Hazod 《Journal of Mathematical Sciences》1999,93(4):531-542
It is shown that weakly convergent sums (products) of normalized i.i.d. random variables with values in a finite-dimensional
vector space or in a group are mixing in the sense of A. Rényi, and limit theorems for random sums with nonindependent indices
are obtained. A new version of H. Robbins' limit theorem for random sums is presented.
Proceedings of the Seminar on Stability Problems for Stochastic Models, Hajdúszoboszló Hungary, 1997, Part III. 相似文献
18.
A. N. Skrypnik 《Journal of Mathematical Sciences》1998,91(3):2990-3001
We consider two functionals of sums of independent random variables and demonstrate that the validity of the central limit
theorem for the sums of independent random variables that enter the arguments of those functionals is a sufficient condition
for one of the functionals and a necessary and sufficient condition for the other one to have a weak limit.
Proceedings of the Seminar on Stability Problems for Stochastic Models. Moscow. Russia. 1996. Part II. 相似文献
19.
In this paper we prove an almost sure limit theorem for random sums of independent random variables in the domain of attraction
of a p-semistable law and describe the limit law. 相似文献
20.
Zinoviy Landsman 《Statistics & probability letters》2011,81(3):382-391
Rogers and Shi (1995) have used the technique of conditional expectations to derive approximations for the distribution of a sum of lognormals. In this paper we extend their results to more general sums of random variables. In particular we study sums of functions of dependent random variables that are multivariate normally distributed and also derive results for sums of functions of dependent random variables from the additive exponential dispersion family. The usefulness of our results for practical applications is also discussed. 相似文献