The Annals of Probability

Quenched asymptotics for Brownian motion in generalized Gaussian potential

Xia Chen

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Abstract

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

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

Dates
First available in Project Euclid: 24 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aop/1393251297

Digital Object Identifier
doi:10.1214/12-AOP830

Mathematical Reviews number (MathSciNet)
MR3178468

Zentralblatt MATH identifier
1294.60101

Subjects
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

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

Citation

Chen, Xia. Quenched asymptotics for Brownian motion in generalized Gaussian potential. Ann. Probab. 42 (2014), no. 2, 576--622. doi:10.1214/12-AOP830. https://projecteuclid.org/euclid.aop/1393251297


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