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1.
This paper obtains some equivalent conditions about the asymptotics for the density of the supremum of a random walk with
light-tailed increments in the intermediate case. To do this, the paper first corrects the proofs of some existing results
about densities of random sums. On the basis of the above results, the paper obtains some equivalent conditions about the
asymptotics for densities of ruin distributions in the intermediate case and densities of infinitely divisible distributions.
In the above studies, some differences and relations between the results on a distribution and its corresponding density can
be discovered.
相似文献
2.
本文研究了NA变量线性形式的强稳定性.利用随机变量的截尾术及强大数定律,得到了一般情况下不同分布NA变量具有强稳定性的充分条件,推广了NA列的Jamison型加权和具有强稳定性的充分条件. 相似文献
3.
在负象限相依结构下,得到了支撵在(-∞,∞)上的(D)族随机变量非中心化以及中心化部分和的精致大偏差.同时,还在较弱的条件下,得到了相应的中心化随机和的精致大偏差. 相似文献
4.
Self-decomposable distributions are given as limits of normalized sums of independent random variables. We define semi-selfdecomposable
distributions as limits of subsequences of normalized sums. More generally, we introduce a way of making a new class of limiting
distributions derived from a class of distributions by taking the limits through subsequences of normalized sums, and define
the class of semi-selfdecomposable distributions and a decreasing sequence of subclasses of it. We give two kinds of necessary
and sufficient conditions for distributions belonging to those classes, one is in terms of the decomposability of random variables
and another is in terms of Lévy measures.
Received: 1 May 1997 / Revised version: 5 February 1998 相似文献
5.
V. M. Kruglov 《Journal of Mathematical Sciences》1995,76(2):2275-2282
Necessary and sufficient conditions are obtained for the weak convergence of nonrandomly centered and normalized random sums
of independent identically distributed random variables. Limit distributions for these sums are described.
Proceedings of the XVI Seminar on Stability Problems for Stochastic Models, Part I, Eger, Hungary, 1994. 相似文献
6.
We improve bounds of accuracy of the normal approximation to the distribution of a sum of independent random variables under relaxed moment conditions, in particular, under the absence of moments of orders higher than the second. We extend these results to Poisson binomial, binomial, and Poisson random sums. Under the same conditions, we obtain bounds for the accuracy of approximation of the distributions of mixed Poisson random sums by the corresponding limit law. In particular, we construct these bounds for the accuracy of approximation of the distributions of geometric, negative binomial, and Poisson-inverse gamma (Sichel) random sums by the Laplace, variance gamma, and Student distributions, respectively. 相似文献
7.
V. M. Kruglov 《Journal of Mathematical Sciences》1996,81(5):2957-2969
Necessary and sufficient conditions are obtained for the weak convergence of random sums and maximum random sums of independent
identically distributed random variables. Limit distributions for these sums are described. The indices are not assumed to
be independent of the summands.
Supported in part by Grants NFW000 and NFW300 from the International Science Foundation and the Russian Government and by
Grant No. 93-011-1446 from the Russian Foundation for Fundamental Research.
Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russia, 1995, Part I. 相似文献
8.
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
9.
Alexey Khartov 《Lithuanian Mathematical Journal》2017,57(2):196-203
We consider sums of independent random variables within the scheme of series. We focus on the case where every summand has a zero mean and finite variance and sums have unit variances. We obtain a criterion of stochastic compactness (defined by W. Feller) for sequences of distributions of such sums. The condition of uniform asymptotic negligibility of summands is not supposed. 相似文献
10.
Arnold and Villaseñor (1999) raised several questions for upper records, including characterizing all limit distributions of normalized partial sums of upper records. We provide some answers in the case when the distribution from which the samples are drawn is bounded above. When the distribution is not bounded above, we give sufficient conditions on the distribution for the properly normalized partial sums to converge to a standard normal distribution. We show that our conditions are general enough so that the examples provided by Arnold and Villaseñor (1999) are covered by our results. 相似文献
11.
《Stochastic Processes and their Applications》2019,129(10):4163-4207
We consider dynamical systems on a finite measure space fulfilling a spectral gap property and Birkhoff sums of a non-negative, non-integrable observable. For such systems we generalize strong laws of large numbers for intermediately trimmed sums only known for independent random variables. The results split up in trimming statements for general distribution functions and for regularly varying tail distributions. In both cases the trimming rate can be chosen in the same or almost the same way as in the i.i.d. case. As an example we show that piecewise expanding interval maps fulfill the necessary conditions for our limit laws. As a side result we obtain strong laws of large numbers for truncated Birkhoff sums. 相似文献
12.
We consider conditions under which the distributions of sequences of integer-valued nonnegative strongly additive functions can be approximated by the distributions of sums of independent random variables.__________Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 2, pp. 270–281, April–June, 2005. 相似文献
13.
冯凤香 《纯粹数学与应用数学》2010,26(4):570-575
利用矩不等式和截尾的方法,讨论了不同分布的φ混合序列的最大值不等式.作为应用,获得了混合序列的一阶矩及p(p〉1)阶矩分别存在有限的充分条件,这是一个与独立同分布情形一致的结果. 相似文献
14.
Fotis Loukissas 《Journal of Theoretical Probability》2012,25(4):913-924
In this paper, we investigate the precise large deviations for sums of independent identically distributed random variables with heavy-tailed distributions. We prove asymptotic relations for non-random sums and for random sums of random variables with long-tailed distributions. We apply the results on two useful counting processes, namely, renewal and compound-renewal processes. 相似文献
15.
We study the properties of subexponential distributions and find new sufficient and necessary conditions for membership in the class of these distributions. We establish a connection between the classes of subexponential and semiexponential distributions and give conditions for preservation of the asymptotics of subexponential distributions for functions of distributions. We address similar problems for the class of the so-called locally subexponential distributions. As an application of these results, we refine the asymptotics of the distribution of the supremum of sequential sums of random variables with negative drift, in particular, local theorems. 相似文献
16.
17.
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
18.
《Journal of Combinatorial Theory, Series A》1987,45(2):277-289
We consider the problem of decomposing a matrix of integers according to constraints on the row and column sums, in the case when the original matrix is infinite. Some necessary conditions and some sufficient conditions are found for the existence of such a decomposition, generalizing results of Ball for the finite case. Connections with the Transversal Problem for infinite sets are pointed out. 相似文献
19.
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
20.
We prove that for almost all sufficient conditions based on degree sums or neighborhood unions of 3-independent sets for a graph G to be hamiltonian imply that the 0-dual closure of G is complete. The proofs are very short. 相似文献