Large deviations for Brownian motion in a random scenery

• 成果类型: Article
• 署名作者: Asselah, A; Castell, F
• 署名单位: Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-003-0265-3
• 发表日期: 2003
• 页码: 497-527
• 关键词: markov process expectations; asymptotic evaluation; anderson model; exact renormalization; mathematical-models; parabolic problems; directed polymers; limit-theorem; DIFFUSIONS; transport

摘要

We prove large deviations principles in large time, for the Brownian occupation time in random scenery 1/t integral(0)(t) xi(B-s) ds. The random field is constant on the elements of a partition of R-d into unit cubes. These random constants, say {xi(j), j is an element of Z(d)} consist of i.i.d. bounded variables, independent of the Brownian motion {B-s, s greater than or equal to 0}. This model is a time-continuous version of Kesten and Spitzer's random walk in random scenery. We prove large deviations principles in quenched'' and annealed'' settings.