Local Times and Related Properties of Multidimensional Iterated Brownian Motion期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

首页 | 本学科首页

官方微博 | 高级检索

Local Times and Related Properties of Multidimensional Iterated Brownian Motion

Authors:

Yimin Xiao

Abstract:

Let {W(t), t isin

R} and {B(t), t

0} be two independent Brownian motions in R with W(0) = B(0) = 0 and let

$$Y(t) = W(B(t)){text{ }}(t geqslant 0)$$

be the iterated Brownian motion. Define d-dimensional iterated Brownian motion by

$X(t) = (X_1 (t),...,X_d (t)){text{ }}(t geqslant 0)$

where X₁, X_d are independent copies of Y. In this paper, we investigate the existence, joint continuity and Hölder conditions in the set variable of the local time

$L = { L(x,B):x in {text{R}}^d ,B in B({text{R}}_{text{ + }} )}$

of X(t), where $B({text{R}}_{text{ + }} )$ is the Borel sgr

-algebra of R₊. These results are applied to study the irregularities of the sample paths and the uniform Hausdorff dimension of the image and inverse images of X(t).

Keywords:

Iterated Brownian motion Local times Hö lder conditions Level set Hausdorff dimension

本文献已被 SpringerLink 等数据库收录！

设为首页 | 免责声明 | 关于勤云 | 加入收藏