The Annals of Probability

Asymptotic Approximations for Brownian Motion Boundary Hitting Times

G. O. Roberts

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Abstract

The problem of approximating boundary hitting times for diffusion processes, and in particular Brownian motion, is considered. Using a combination of probabilistic and function-analytic techniques, approximations for conditioned diffusion distributions are obtained. These lead to approximations for the distribution of the hitting time itself. The approximations are split into three cases depending on whether the boundary is upper case, approximation square root or lower case, and one-sided boundaries are also considered separately.

Article information

Source
Ann. Probab., Volume 19, Number 4 (1991), 1689-1731.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176990230

Digital Object Identifier
doi:10.1214/aop/1176990230

Mathematical Reviews number (MathSciNet)
MR1127722

Zentralblatt MATH identifier
0739.60074

JSTOR
links.jstor.org

Subjects
Primary: 60J65: Brownian motion [See also 58J65]
Secondary: 60J50: Boundary theory

Keywords
Brownian motion boundary hitting time upper case lower case eigenfunction expansion

Citation

Roberts, G. O. Asymptotic Approximations for Brownian Motion Boundary Hitting Times. Ann. Probab. 19 (1991), no. 4, 1689--1731. doi:10.1214/aop/1176990230. https://projecteuclid.org/euclid.aop/1176990230


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