On almost sure convergence of the quadratic variation of Brownian motion

被引：2

作者：

Levental, S ^{[1
]}

Erickson, RV ^{[1
]}

机构：

[1] Michigan State Univ, Dept Stat & Probabil, E Lansing, MI 48824 USA

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2003年 / 106卷 / 02期

关键词：

Brownian motion; quadratic variation; a.s; convergence;

D O I：

10.1016/S0304-4149(03)00048-6

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：

We study the problem of a.s. convergence of the quadratic variation of Brownian motion. We present some new sufficient and necessary conditions for the convergence. As a byproduct we get a new proof of the convergence in the case of refined partitions, a result that is due to Levy. Our method is based on conversion of the problem to that of a Gaussian sequence via decoupling. (C) 2003 Elsevier Science B.V. All rights reserved.

引用

页码：317 / 333

页数：17

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