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
收藏
页码：317 / 333
页数：17
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