|
MSpace at the University of Manitoba >
Faculty of Graduate Studies (Electronic Theses and Dissertations) >
FGS - Electronic Theses & Dissertations (Public) >
Please use this identifier to cite or link to this item:
http://hdl.handle.net/1993/8123
|
| Title: | Linear and non-linear boundary crossing probabilities for Brownian motion and related processes |
| Authors: | Wu, Tung-Lung Jr |
| Supervisor: | Fu, James C. (Statistics) |
| Examining Committee: | Wang, Liqun (Statistics) Johnson, Brad (Statistics) Guo, Benqi (Mathematics) Li, Gang (Animas Corporation | LifeScan, Inc. | Johnson & Johnson ) |
| Graduation Date: | October 2012 |
| Keywords: | boundary crossing probabilities
Brownian motion
first passage time
finite Markov chain imbedding
diffusion processes
absorption probability
transition probability matrices
random walks |
| Issue Date: | Dec-2010 |
| Publisher: | Applied Probability Trust - Journal of Applied Probability |
| Citation: | Fu, J. C. and Wu, T.-L. (2010). Linear and nonlinear boundary crossing probabilities for Brownian motion and related processes. J. Appl. Prob., 47, 1058-1071. |
| Abstract: | 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. |
| URI: | http://hdl.handle.net/1993/8123 |
| Appears in Collections: | FGS - Electronic Theses & Dissertations (Public)
|
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.
|
