The first exit time of a Brownian motion from an unbounded convex domain
type: Item
instance of: scholarly article
title: The first exit time of a Brownian motion from an unbounded convex domain
zbMATH Open document ID: 1030.60032
author: Wenbo V. Li
published in: The Annals of Probability
publication date: 2004-02-08T00:00:00Z
review text: Let \(\tau_D\) be the first exit time of a \((d+1)\)-dimensional Brownian motion from an unbounded open domain \(D= \{(x,y)\in \mathbb{R}^{d+1}\mid y> f(x),\;x\in \mathbb{R}^d\}\) starting at \((x_0,f(x_0)+ 1)\in \mathbb{R}^{d+1}\) for some \(x_0\in \mathbb{R}^d\), where the function \(f(.)\) on \(\mathbb{R}^d\) is convex and \(f(x)\to\infty\) as the Euclidean norm \(|x|\to\infty\). The author determines a general estimation for the asymptotics of \(\log P(\tau_D> t)\) by using Gaussian techniques.
Mathematics Subject Classification ID: 60G40
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 1933041
zbMATH Keywords: Brownian motion
zbMATH Keywords: Gaussian techniques
reviewed by: Ion C. Vladimirescu
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1048516546
OpenAlex ID: W1977927939
cites work: Large time asymptotics for Brownian hitting densities of transient concave curves
cites work: Brownian motion in cones
cites work: The first exit time of planar Brownian motion from the interior of a parabola
cites work: Brownian motion with lower class moving boundaries which grow faster than t**(1/2)
cites work: Small ball estimates for Brownian motion under a weighted sup-norm
cites work: Exit times of Brownian motion, harmonic majorization, and Hardy spaces
cites work: Quadratic functionals and small ball probabilities for the \(m\)-fold integrated Brownian motion
cites work: A functional LIL for symmetric stable processes.
cites work: First Passage times and Sojourn Times for Brownian Motion in Space and the Exact Hausdorff Measure of the Sample Path
cites work: Exit times from cones in \({\mathbb{R}}^ n\) of Brownian motion
cites work: Q3802106
cites work: The first-passage density of a continuous gaussian process to a general boundary
cites work: The first-passage density of the Brownian motion process to a curved boundary
cites work: Q4032143
cites work: One-Sided Boundary Crossing for Processes with Independent Increments
cites work: Q4027481
cites work: Metric entropy and the small ball problem for Gaussian measures
cites work: First exist times from moving boundaries for sums of independent random variables
cites work: First exit time of a random walk from the bounds \(f(n)\pm cg(n)\), with applications
cites work: Q3997990
cites work: Boundary crossing of Brownian motion. Its relation to the law of the iterated logarithm and to sequential analysis
cites work: Small deviations for Gaussian Markov processes under the sup-norm
cites work: Small ball probabilities for Gaussian Markov processes under the \(L_p\)-norm.
cites work: Approximation, metric entropy and small ball estimates for Gaussian measures
cites work: Gaussian processes: Inequalities, small ball probabilities and applications
cites work: Lower tail probabilities for Gaussian processes.
cites work: A normal comparison inequality and its applications
cites work: Q4841584
cites work: Q4139359
cites work: Small Deviations in a Space of Trajectories
cites work: ON ESTIMATES AND THE ASYMPTOTIC BEHAVIOR OF NONEXIT PROBABILITIES OF A WIENER PROCESS TO A MOVING BOUNDARY
cites work: Small deviations of Gaussian process
cites work: Approximations of boundary crossing probabilities for a Brownian motion
cites work: Probability bounds for first exists through moving boundaries
cites work: Small ball probabilities for a Wiener process under weighted sup-norms, with an application to the supremum of Bessel local times
cites work: Some Theorems Concerning 2-Dimensional Brownian Motion
cites work: Brownian first exit from and sojourn over one sided moving boundary and application
DOI: 10.1214/AOP/1048516546
description: scientific article; zbMATH DE number 1933041