共查询到20条相似文献,搜索用时 15 毫秒
1.
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
2.
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
3.
LiXin Zhang 《中国科学 数学(英文版)》2016,59(12):2503-2526
Kolmogorov’s exponential inequalities are basic tools for studying the strong limit theorems such as the classical laws of the iterated logarithm for both independent and dependent random variables. This paper establishes the Kolmogorov type exponential inequalities of the partial sums of independent random variables as well as negatively dependent random variables under the sub-linear expectations. As applications of the exponential inequalities, the laws of the iterated logarithm in the sense of non-additive capacities are proved for independent or negatively dependent identically distributed random variables with finite second order moments. For deriving a lower bound of an exponential inequality, a central limit theorem is also proved under the sub-linear expectation for random variables with only finite variances. 相似文献
4.
Sharpened versions of a Kolmogorov’s inequality for sums of independent Bernoulli random variables are proved. 相似文献
5.
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
6.
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
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.
研究了服从长尾分布族上的随机变量和的精确大偏差问题,其中假设代表索赔额的随机变量序列是一列宽上限相依的、不同分布的随机变量序列。在给定一些假设条件下,得到了部分和与随机和的两种一致渐近结论。 相似文献
9.
Krzysztof Oleszkiewicz 《Israel Journal of Mathematics》2014,203(1):429-443
A precise deviation inequality in terms of weak moments is proved for Rademacher sums. It yields an asymptotic equality of the optimal constants in the Khinchin and Khinchin-Kahane inequalities. Tail bounds of similar nature and estimates for linear combinations of Steinhaus random variables are also discussed. 相似文献
10.
Jason Fulman 《Annals of Combinatorics》2006,10(3):319-332
Bolthausen used a variation of Stein’s method to give an inductive proof of the Berry-Esseen theorem for sums of independent,
identically distributed random variables. We modify this technique to prove a Berry-Esseen theorem for character ratios of
a random representation of the symmetric group on transpositions. An analogous result is proved for Jack measure on partitions.
Received March 11, 2005 相似文献
11.
We prove a theorem on the strong law of large numbers for martingales. The existence of higher moments is not assumed. From the theorem proved, we deduce numerous well-known results on the strong law of large numbers both for martingales and for sequences of sums of independent random variables. 相似文献
12.
M. N. Marushin 《Mathematical Notes》1971,10(2):535-539
Sums of arbitrarily dependent random variables are investigated, and a lemma due to Bernshtein concerning the normal-distribution limit theorem is proved for such sums.Translated from Matematicheskie Zametki, Vol. 10, No. 2, pp. 187–194, August, 1971. 相似文献
13.
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
14.
15.
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
16.
华志强 《纯粹数学与应用数学》2015,(4):360-366
从保险的实际出发,研究服从长尾分布族(L族)上的多元风险模型中随机变量序列的部分和的精确大偏差,其中假设随机变量序列是一列延拓负相依(END)的、同分布的随机变量序列,利用基于求L族的精确大偏差的方法得到了随机变量部分和的渐近下界. 相似文献
17.
In 1952 Darling proved the limit theorem for the sums of independent identically distributed random variables without power moments under the functional normalization. This paper contains an alternative proof of Darling’s theorem, using the Laplace transform. Moreover, the asymptotic behavior of probabilities of large deviations is studied in the pattern under consideration. 相似文献
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19.
Georgios Psarrakos 《Insurance: Mathematics and Economics》2010,47(3):428-433
In 1988, Shanthikumar proved that the sum of a geometrically distributed number of i.i.d. DFR random variables is also DFR. In this paper, motivated by the inverse problem, we study monotonicity properties related to defective renewal equations, and obtain that if a compound geometric distribution is DFR, then the random variables of the sums are NWU (a class that contains DFR). Furthermore, we investigate some applications of risk theory and give a characterization of the exponential distribution. 相似文献
20.