Unified limit theorems for increments of processes with independent increments

被引：2

作者：

Frolov, AN ^{[1
]}

机构：

[1] St Petersburg State Univ, Dept Math & Mech, St Petersburg 198504, Russia

来源：

THEORY OF PROBABILITY AND ITS APPLICATIONS | 2004年 / 49卷 / 03期

关键词：

increments of processes with independent increments; Erdos-Renyi law; Shepp law; the law of large numbers; the law of the iterated logarithm;

D O I：

10.1137/S0040585X9798124X

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

A unified theory is constructed which describes the a.s. (almost surely) behavior of increments of stochastically continuous homogeneous processes with independent increments. This theory includes the strong law of large numbers, the Erdos-Renyi law, the Shepp law, the Csorgo Revesz law, and the law of the iterated logarithm. The range of applicability of the results is extended from several particular cases to the whole class of stochastically continuous homogeneous processes with independent increments.

引用

页码：531 / 540

页数：10

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