An almost sure invariance principle for random walks in a space-time random environment

• 成果类型: Article
• 署名作者: Rassoul-Agha, F; Seppalainen, T
• 署名单位: University System of Ohio; Ohio State University; University of Wisconsin System; University of Wisconsin Madison; Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-004-0424-1
• 发表日期: 2005
• 页码: 299-314
• 关键词: CENTRAL-LIMIT-THEOREM; additive-functionals

摘要

We consider a discrete time random walk in a space-time i.i.d. random environment. We use a martingale approach to show that the walk is diffusive in almost every fixed environment. We improve on existing results by proving an invariance principle and considering environments with an L-2 averaged drift. We also state an a.s. invariance principle for random walks in general random environments whose hypothesis requires a subdiffusive bound on the variance of the quenched mean, under an ergodic invariant measure for the environment chain.