Large deviations for Brownian motion on the Sierpinski gasket

被引：0

作者：

Ben Arous, G

Kumagai, T ^{[1
]}

机构：

[1] Kyoto Univ, Grad Sch Informat, Kyoto 6068501, Japan

[2] Ecole Polytech Fed Lausanne, Dept Math, CH-1015 Lausanne, Switzerland

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2000年 / 85卷 / 02期

关键词：

large deviation; diffusion; Sierpinski gasket; fractal; branching process;

D O I：

暂无

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 large deviations for Brownian motion on the Sierpinski gasket in the short time limit. Because of the subtle oscillation of hitting times of the process, no large deviation principle can hold. In fact, our result shows that there is an infinity of different large deviation principles for different subsequences, with different (good) rate functions. Thus, instead of taking the time scaling epsilon --> 0, we prove that the large deviations hold for E-n(z) = (2/5)(n)z as n --> infinity, using one parameter family of rate functions I-z (z is an element of [2/5, 1)). As a corollary, we obtain Strassen-type laws of the iterated logarithm. (C) 2000 Elsevier Science B.V. All rights reserved. MSG. 60F10; 60J60; 60J80.

引用

页码：225 / 235

页数：11

共 15 条

[1] Brownian motion and harmonic analysis on Sierpinski carpets [J].