Multidimensional hitting time results for Brownian bridges with moving hyperplanar boundaries
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Authors
Atkinson, Michael P.
Singham, Dashi I.
Subjects
Brownian bridge
First-passage time
Hyperplane boundaries
First-passage time
Hyperplane boundaries
Advisors
Date of Issue
2015
Date
Publisher
Elsevier
Language
en_US
Abstract
We calculate several hitting time probabilities for a correlated multidimensional Brownian bridge process, where the boundaries are hyperplanes that move linearly with time. We compute the probability that a Brownian bridge will cross a moving hyperplane if the end- points of the bridge lie on the same side of the hyperplane at the starting and ending times, and we derive the distribution of the hitting time if the endpoints lie on opposite sides of the moving hyperplane. Our third result calculates the probability that this process remains between two parallel hyperplanes, and we extend this result in the independent case to a hyperrectangle with moving faces. To derive these quantities, we rotate the coordinate axes to transform the problem into a one-dimensional calculation.
Type
Article
Description
The article of record may be found at: http://dx.doi.org/10.1016/j.spl.2015.02.006
Series/Report No
Department
Operations Research (OR)
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
Funder
Format
84 p.
Citation
M.P. Atkinson, D.I. Singham, "Multidimensional hitting time results for Brownian bridges with moving hyperplane boundaries," Statistics and Probability Letters, v.100, (2015), pp. 85-92.
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.