| 王文胜.关于Wiener过程泛函连续模的精确收敛速度(英文)[J].数学研究及应用,2002,22(4):507~514 |
| 关于Wiener过程泛函连续模的精确收敛速度(英文) |
| Exact Convergence Rates of Functional Modulus of Continuity of a Wiener Process |
| 投稿时间：1999-09-14 |
| DOI：10.3770/j.issn:1000-341X.2002.04.001 |
| 中文关键词: |
| 英文关键词:Wiener process functional modulus of continuity modulus of non-differentiability |
| 基金项目: |
|
| 摘要点击次数: 2132 |
| 全文下载次数: 1251 |
| 中文摘要: |
| 设{W（t）,t≥0}是一标准Wiener过程,记S是Strassen重对数律的紧集类·本文中我们讨论了两个变量sup0≤t≤1-h inff∈S sup0≤x≤1 |(W(t+hx)-W(t))(2h log h-1)-1/2 - f(x)|及inf0≤t≤1-h sup0≤x≤1 |(W(t + hx) - W(t))(2hlogh-1)-1/2- f(x)|（对任何f∈S）趋于零的精确的收敛速度.作为一个推广,我们建立了Wiener过程的不可微模与泛函的连续模之间的一种关系. |
| 英文摘要: |
| Let {W(t),t ≥ 0} be a standard Wiener process and S be the set of Strassen'sfunctions. In this paper we investigate the exact rates of convergence to zero of thevariables sup0≤t≤1-h inff∈S sup0≤x≤1 |(W(t+hx)-W(t))(2h log h-1)-1/2 - f(x)| and inf0≤t≤1-h sup0≤x≤1 |(W(t + hx) - W(t))(2hlogh-1)-1/2- f(x)| for any f ∈ S. As aconsequence, a relation between the modulus of non-differentiability and the fiunctionalmodulus of continuity for a Wiener process is established. |
| 查看全文 查看/发表评论 下载PDF阅读器 |
