Asymptotic behavior of increments of random fields

被引：1

作者：

Frolov A.N. ^{[1
]}

机构：

[1] St. Petersburg State University, St. Petersburg

来源：

Journal of Mathematical Sciences | 2005年 / 128卷 / 1期

关键词：

Asymptotic Behavior; Random Field; Iterate Logarithm; Exponential Moment; Multidimensional Index;

D O I：

10.1007/s10958-005-0209-9

中图分类号：

学科分类号：

摘要：

We derive universal strong laws for increments of sums of i.i.d. random variables with multidimensional indices without an exponential moment. Our theorems yield the strong law of large numbers, the law of the iterated logarithm, and the Csorgo-Revesz laws for random fields. New results are obtained for distributions from domains of attraction of the normal law and of completely asymmetric stable laws with index α (1, 2). Bibliography: 18 titles. ©2005 Springer Science+Business Media, Inc.

引用

页码：2604 / 2613

页数：9

共 18 条

[1] Erdos P., Renyi A., On a new law of large numbers, J. Analyse Math., 23, pp. 103-111, (1970)
[2] Shepp L.A., A limit law concerning moving averages, Ann. Math. Statist., 35, pp. 424-428, (1964)
[3] Csorgo S., Erdo″s-Rényi laws, Ann. Statist., 7, pp. 772-787, (1979)
[4] Deheuvels P., Devroye L., Limit laws of Erdo″s-Rényi-Shepp type, Ann. Probab., 15, pp. 1363-1386, (1987)
[5] Mason D.M., An extended version of the Erdo″s-Rényi strong law of large numbers, Ann. Probab., 17, pp. 257-265, (1989)
[6] Csorgo M., Revesz P., Strong Approximations in Probability and Statistics, (1981)
[7] Zinchenko N.M., The asymptotics of increments of stable stochastic processes with jumps of one sign, Teor. Veroyatn. Primen., 32, pp. 793-796, (1987)
[8] Frolov A.N., On one-sided strong laws for large increments of sums, Statist. Probab. Lett., 37, pp. 155-165, (1998)
[9] Frolov A.N., On asymptotic behavior of increments of sums of independent random variables, Dokl. RAN, 372, pp. 596-599, (2000)
[10] Frolov A.N., On one-sided strong laws for increments of sums of i.i.d. random variables, Studia Sci. Math. Hungar., 39, pp. 333-359, (2002)

← 1 2 →