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Boundary crossing probabilities for high-dimensional Brownian motion

  • James C. Fu (a1) and Tung-Lung Wu (a2)


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.


Corresponding author

* 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:


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Boundary crossing probabilities for high-dimensional Brownian motion

  • James C. Fu (a1) and Tung-Lung Wu (a2)


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