The Annals of Probability

Second-Order Approximations to the Density, Mean and Variance of Brownian First-Exit Times

Christel Jennen

Full-text: Open access

Abstract

This paper presents correction terms to the tangent approximation for the first-exit density of Brownian motion at distant boundaries. These lead to second-order approximations to the first-exit distribution. Asymptotic formulas for the mean and variance of the first-exit time are derived. Numerical comparisons show the accuracy of the approximations.

Article information

Source
Ann. Probab., Volume 13, Number 1 (1985), 126-144.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993071

Digital Object Identifier
doi:10.1214/aop/1176993071

Mathematical Reviews number (MathSciNet)
MR770633

Zentralblatt MATH identifier
0567.62068

JSTOR
links.jstor.org

Subjects
Primary: 62L10: Sequential analysis
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 60J65: Brownian motion [See also 58J65]

Keywords
First-exit time Brownian motion sequential tests

Citation

Jennen, Christel. Second-Order Approximations to the Density, Mean and Variance of Brownian First-Exit Times. Ann. Probab. 13 (1985), no. 1, 126--144. doi:10.1214/aop/1176993071. https://projecteuclid.org/euclid.aop/1176993071


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