Stochastic area for Brownian motion on the Sierpinski gasket
成果类型：
Article
署名作者：
Hambly, BM; Lyons, TJ
署名单位：
University of Edinburgh; Imperial College London
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
发表日期：
1998
页码：
132-148
关键词：
摘要：
We construct a Levy stochastic area for Brownian motion on the Sierpinski gasket. The standard approach via Ito integrals fails because this diffusion has sample paths which are far rougher than those of semimartingales. We thus provide an example demonstrating the restrictions of the semimartingale framework. As a consequence of the existence of the area one has a stochastic calculus and can solve stochastic differential equations driven by Brownian motion on the Sierpinski gasket.