Multidimensional hitting time results for Brownian bridges with moving hyperplanar boundaries
Article (378.0Kb)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.
Description
The article of record may be found at: http://dx.doi.org/10.1016/j.spl.2015.02.006
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.Collections
Related items
Showing items related by title, author, creator and subject.
-
Tropical Support Vector Machine and its Applications to Phylogenomics
(ArXiv, 2020);Most data in genome-wide phylogenetic analysis (phylogenomics) is essentially multidimensional, posing a major challenge to human comprehension and computational analysis. Also, we can not directly apply statistical learning ... -
Extremal positive semidefinite matrices whose sparsity pattern is given by graphs without K5 minors
(Elsevier, 2016);For a graph G with p vertices the closed convex cone S≽0(G) consists of all real positive semidefinite p × p matrices whose sparsity pattern is given by G, that is, those matrices with zeros in the off-diagonal entries ... -
Magnetic force on a current carrying wire - Jumping wire physics demonstration [video]
(2015);Magnetic Force on a current carrying wire Hi. I’m Dr. Bruce Denardo here in the Physics Department of the Naval Postgraduate School in Monterey, California. In another video, we demonstrated the fundamental magnetic force ...
