The Annals of Probability

Quenched asymptotics for Brownian motion in generalized Gaussian potential

Xia Chen

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

https://projecteuclid.org/euclid.aop/1393251297

Digital Object Identifier
doi:10.1214/12-AOP830

Mathematical Reviews number (MathSciNet)
MR3178468

Zentralblatt MATH identifier
1294.60101

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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