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February 2002 Inverse method of images
Violet S.F. Lo, Gareth O. Roberts, Henry E. Daniels
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Bernoulli 8(1): 53-80 (February 2002).


We consider the problem of approximating the density of the time at which a Brownian path first crosses a curved boundary in cases where the exact density is not known or is difficult to compute. Approximation methods which involve the use of images will be proposed. These methods can be used not only for one-sided boundaries but also for the case of two-sided boundaries; not only for concave boundaries but also for convex boundaries. The square root boundary and parabolic boundary provide examples for numerical comparisons of the approximation methods.


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Violet S.F. Lo. Gareth O. Roberts. Henry E. Daniels. "Inverse method of images." Bernoulli 8 (1) 53 - 80, February 2002.


Published: February 2002
First available in Project Euclid: 10 March 2004

zbMATH: 1001.60084
MathSciNet: MR2003H:60120

Keywords: boundary crossing probabilities , Brownian motion , method of images

Rights: Copyright © 2002 Bernoulli Society for Mathematical Statistics and Probability

Vol.8 • No. 1 • February 2002
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