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Boundary Crossing Probability for Brownian Motion and General Boundaries
Liqun Wang and Klaus Pötzelberger
Journal of Applied Probability
Vol. 34, No. 1 (Mar., 1997), pp. 54-65
Published by: Applied Probability Trust
Stable URL: http://www.jstor.org/stable/3215174
Page Count: 12
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An explicit formula for the probability that a Brownian motion crosses a piecewise linear boundary in a finite time interval is derived. This formula is used to obtain approximations to the crossing probabilities for general boundaries which are the uniform limits of piecewise linear functions. The rules for assessing the accuracies of the approximations are given. The calculations of the crossing probabilities are easily carried out through Monte Carlo methods. Some numerical examples are provided.
Journal of Applied Probability © 1997 Applied Probability Trust