QUENCHED ASYMPTOTICS FOR BROWNIAN MOTION OF RENORMALIZED POISSON POTENTIAL AND FOR THE RELATED PARABOLIC ANDERSON MODELS

• 成果类型: Article
• 署名作者: Chen, Xia
• 署名单位: University of Tennessee System; University of Tennessee Knoxville
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/11-AOP655
• 发表日期: 2012
• 页码: 1436-1482
• 关键词: lyapunov exponent; intermittency; environment

摘要

Let B-s be a d-dimensional Brownian motion and omega(dx) be an independent Poisson field on R-d. The almost sure asymptotics for the logarithmic moment generating function logE(0) exp{+/-theta integral(t)(0)(V) over bar (B-s)ds} (t -> infinity) are investigated in connection with the renormalized Poisson potential of the form (V) over bar (x) = integral(Rd) 1/vertical bar y - x vertical bar(p)[omega(dy) - dy], x is an element of R-d. The investigation is motivated by some practical problems arising from the models of Brownian motion in random media and from the parabolic Anderson models.