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Boundary crossing probabilities for high-dimensional Brownian motion

Part of: Markov processes

Published online by Cambridge University Press:  21 June 2016

James C. Fu  and
Tung-Lung Wu
James C. Fu*
Affiliation:
University of Manitoba
Tung-Lung Wu*
Affiliation:
Mississippi State University
*
* Postal address: Department of Statistics, University of Manitoba, Winnipeg, MB R3T 2N2, Canada.
** Postal address: Department of Mathematics and Statistics, Mississippi State University, Starkville, MS 39759, USA. Email address: comehome1981@gmail.com
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Abstract

The two-sided nonlinear boundary crossing probabilities for one-dimensional Brownian motion and related processes have been studied in Fu and Wu (2010) based on the finite Markov chain imbedding technique. It provides an efficient numerical method to computing the boundary crossing probabilities. In this paper we extend the above results for high-dimensional Brownian motion. In particular, we obtain the rate of convergence for high-dimensional boundary crossing probabilities. Numerical results are also provided to illustrate our results.

Keywords

Boundary crossing probabilityfinite Markov chain imbeddingBrownian motionY-type time tunnelirregular boundarytwo-dimensionalhigh-dimensionalrate of convergence

MSC classification

Primary: 60J65: Brownian motion
Secondary: 60J60: Diffusion processes 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 2 , June 2016 , pp. 543 - 553
Copyright
Copyright © Applied Probability Trust 2016 

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