Some conditional crossing results of Brownian motion over a piecewise-linear boundary
Explicit formulae are found for the probability that the Brownian motion, Bt, up-crosses, in [0,T], a piecewise-linear function S(t), with the condition that the value of Bt is assigned at a future time u>T or at an intermediate time u<T. Also, the analogous conditional probability concerning Bt is obtained. These results permit to obtain an explicit expression for the first-passage-time distribution function of the generalized Brownian bridge, over S(t).
Year of publication: |
2002
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Authors: | Abundo, Mario |
Published in: |
Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 58.2002, 2, p. 131-145
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Publisher: |
Elsevier |
Subject: | Boundary-crossing probability First-passage-time Piecewise-linear boundary |
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