Brownian motion with singular drift

• 成果类型: Article
• 署名作者: Bass, RF; Chen, ZQ
• 署名单位: University of Connecticut; University of Washington; University of Washington Seattle
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2003
• 页码: 791-817
• 关键词: elliptic-equations; coefficients

摘要

where W-t is d-dimensional Brownian motion with d greater than or equal to 2 and the ith component of At is a process of bounded variation that stands in the same relationship to a measure pi(i) as integral(0)(t) f(X-s) ds does to the measure f (x) dx. We prove weak existence and uniqueness for the above stochastic differential equation when the measures pi(i) are members of the Kato class Kd-1. As a typical example, we obtain a Brownian motion that has upward drift when in certain fractal-like sets and show that such a process is unique in law.