Limit velocity and zero-one laws for diffusions in random environment

• 成果类型: Article
• 署名作者: Goergen, Laurent
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051606000000051
• 发表日期: 2006
• 页码: 1086-1123
• 关键词: random-walks; large numbers; homogenization; BEHAVIOR

摘要

We prove that multidimensional diffusions in random environment have a limiting velocity which takes at most two different values. Further, in the two-dimensional case we show that for any direction, the probability to escape to infinity in this direction equals either zero or one. Combined with our results on the limiting velocity, this implies a strong law of large numbers in two dimensions.