Year: 2018
Type: preprint
Abstract: Consider the first exit time of one-dimensional Brownian motion $\{B_s\}_{s\geq 0}$ from a random passageway. We discuss a Brownian motion with two time-dependent random boundaries in quenched sense. Let $\{W_s\}_{s\geq 0}$ be an other one-dimensional Brownian motion independent of $\{B_s\}_{s\geq 0}$ and let $\bfP(\cdot|W)$ represent the conditional probability depending on the realization of $\{W_s\}_{s\geq 0}$. We show that $$-t^{-1}\ln\bfP^x(\forall_{s\in[0,t]}a+βW_s\leq B_s\leq b+βW_s|W)$$ converges to a finite positive constant $γ(β)(b-a)^{-2}$ almost surely and in $L^p~ (p\geq 1)$ if $a
Source: arXiv (Cornell University)
Author: Lv, You
Institution: Beijing Normal University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G672148494, G7633672993
OpenAlex ID: W2785770652