Quenched asymptotics for Brownian motion in generalized Gaussian potential

Xia Chen

doi:10.1214/12-AOP830

Quenched asymptotics for Brownian motion in generalized Gaussian potential

Probability 2014-02-26 v1

Authors: Xia Chen

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Abstract

In this paper, we study the long-term asymptotics for the quenched moment $\mathbb{E}_x\exp \biggl\{\int_0^tV(B_s)\,ds\biggr\}$ consisting of a $d$ -dimensional Brownian motion $\{B_s;s\ge 0\}$ 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.

Keywords

brownian motion

Cite

@article{arxiv.1402.6167,
  title  = {Quenched asymptotics for Brownian motion in generalized Gaussian potential},
  author = {Xia Chen},
  journal= {arXiv preprint arXiv:1402.6167},
  year   = {2014}
}

Comments

Published in at http://dx.doi.org/10.1214/12-AOP830 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Quenched asymptotics for Brownian motion in generalized Gaussian potential

Abstract

Keywords

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