Concentration for multidimensional diffusions and their boundary local times

• 成果类型: Article
• 署名作者: Pal, Soumik
• 署名单位: University of Washington; University of Washington Seattle
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-011-0368-1
• 发表日期: 2012
• 页码: 225-254
• 关键词: transportation-cost inequalities; information inequalities; skorokhod problem; particle-systems; convex duality; path spaces

摘要

We prove that probability laws of certain multidimensional semimartingales which includes time-inhomogenous diffusions, under suitable assumptions, satisfy quadratic transportation cost inequality under the uniform metric. From this we derive concentration properties of Lipschitz functions of process paths that depend on the entire history. In particular, we estimate concentration of boundary local time of reflected Brownian motions on a polyhedral domain. We work out explicit applications of consequences of measure concentration for the case of Brownian motion with rank-based drifts.