QUENCHED ASYMPTOTICS FOR BROWNIAN MOTION IN GENERALIZED GAUSSIAN POTENTIAL

• 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: 10.1214/12-AOP830
• 发表日期: 2014
• 页码: 576-622
• 关键词: parabolic anderson model; large deviations; heat-equation; intermittency; polymer; noise

摘要

In this paper, we study the long-term asymptotics for the quenched moment E-x exp{integral(t)(0) V (B-s) ds} consisting of a d-dimensional Brownian motion {B-s; s >= 0} and a generalized Gaussian field V. The major progress made in this paper includes: Solution to an open problem posted by Carmona and Molchanov [Probab. Theory Related Fields 102 (1995) 433-453], the quenched laws for Brownian motions in Newtonian-type potentials and in the potentials driven by white noise or by fractional white noise.