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Linear and non-linear boundary crossing probabilities for Brownian motion and related processes

We propose a simple and general method to obtain the boundary crossing probability
for Brownian motion. This method can be easily extended to higher dimensional
of Brownian motion. It also covers certain classes of stochastic processes associated
with Brownian motion. The basic idea of the method is based on being able to
construct a nite Markov chain such that the boundary crossing probability of
Brownian motion is obtained as the limiting probability of the nite Markov chain
entering a set of absorbing states induced by the boundary. Numerical results are
given to illustrate our method.

Identiferoai:union.ndltd.org:MANITOBA/oai:mspace.lib.umanitoba.ca:1993/8123
Date12 1900
CreatorsWu, Tung-Lung Jr
ContributorsFu, James C. (Statistics), Wang, Liqun (Statistics) Johnson, Brad (Statistics) Guo, Benqi (Mathematics) Li, Gang (Animas Corporation | LifeScan, Inc. | Johnson & Johnson )
PublisherApplied Probability Trust - Journal of Applied Probability
Source SetsUniversity of Manitoba Canada
Detected LanguageEnglish

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