The Annals of Probability

Quenched asymptotics for Brownian motion in generalized Gaussian potential

Xia Chen

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In this paper, we study the long-term asymptotics for the quenched moment

\[\mathbb{E}_{x}\exp \biggl\{\int_{0}^{t}V(B_{s})\,ds\biggr\}\]

consisting of a $d$-dimensional Brownian motion $\{B_{s};s\ge0\}$ 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.

Article information

Ann. Probab., Volume 42, Number 2 (2014), 576-622.

First available in Project Euclid: 24 February 2014

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Zentralblatt MATH identifier

Primary: 60J65: Brownian motion [See also 58J65] 60K37: Processes in random environments 60K40: Other physical applications of random processes 60G55: Point processes 60F10: Large deviations

Generalized Gaussian field white noise fractional white noise Brownian motion parabolic Anderson model Feynman–Kac representation


Chen, Xia. Quenched asymptotics for Brownian motion in generalized Gaussian potential. Ann. Probab. 42 (2014), no. 2, 576--622. doi:10.1214/12-AOP830.

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