Open Access
Translator Disclaimer
March 2014 Quenched asymptotics for Brownian motion in generalized Gaussian potential
Xia Chen
Ann. Probab. 42(2): 576-622 (March 2014). DOI: 10.1214/12-AOP830

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.

Citation

Download Citation

Xia Chen. "Quenched asymptotics for Brownian motion in generalized Gaussian potential." Ann. Probab. 42 (2) 576 - 622, March 2014. https://doi.org/10.1214/12-AOP830

Information

Published: March 2014
First available in Project Euclid: 24 February 2014

zbMATH: 1294.60101
MathSciNet: MR3178468
Digital Object Identifier: 10.1214/12-AOP830

Subjects:
Primary: 60F10, 60G55, 60J65, 60K37, 60K40

Rights: Copyright © 2014 Institute of Mathematical Statistics

JOURNAL ARTICLE
47 PAGES


SHARE
Vol.42 • No. 2 • March 2014
Back to Top