A note on the almost sure limit theorem for the product of partial sums

被引：42

作者：

Gonchigdanzan, K

Rempala, GA ^{[1
]}

机构：

[1] Univ Louisville, Dept Math, Louisville, KY 40292 USA

[2] Univ Wisconsin, Dept Math & Comp, Stevens Point, WI 54481 USA

来源：

APPLIED MATHEMATICS LETTERS | 2006年 / 19卷 / 02期

关键词：

almost sure central limit theorem; logarithmic average; partial sums;

D O I：

10.1016/j.aml.2005.06.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present an almost sure limit theorem for the product of the partial sums of i.i.d. positive random variables. We also prove a corresponding almost sure limit theorem for a triangular array. (C) 2005 Elsevier Ltd. All rights reserved.

引用

页码：191 / 196

页数：6

共 8 条

[1]

Arnold B.C., 1999, EXTREMES, V1, P351, DOI [10.1023/A:1009933902505, DOI 10.1023/A:1009933902505]

[2] SOME LIMIT-THEOREMS IN LOG DENSITY [J].

BERKES, I ;

DEHLING, H .

ANNALS OF PROBABILITY, 1993, 21 (03) :1640-1670

[3] Results and problems related to the pointwise central limit theorem [J].

Berkes, I .

ASYMPTOTIC METHODS IN PROBABILITY AND STATISTICS: A VOLUME IN HONOUR OF MIKLOS CSORGO, 1998, :59-96

[4] A NOTE ON THE ALMOST SURE CENTRAL-LIMIT-THEOREM [J].

LACEY, MT ;

PHILIPP, W .

STATISTICS & PROBABILITY LETTERS, 1990, 9 (03) :201-205

[5] Limit distributions for products of sums [J].

Qi, YC .

STATISTICS & PROBABILITY LETTERS, 2003, 62 (01) :93-100

[6] ASYMPTOTICS FOR PRODUCTS OF SUMS AND U-STATISTICS [J].

Rempala, Grzegorz ;

Wesolowski, Jacek .

ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2002, 7 :47-54

[7]

Resnick S.I., 1973, STOCH PROC APPL, V1, P67

[8]

Weber M., 2000, EXPO MATH, V18, P97

← 1 →