Linear and non-linear boundary crossing probabilities for Brownian motion and related processes
| dc.contributor.author | Wu, Tung-Lung Jr | |
| dc.contributor.examiningcommittee | Wang, Liqun (Statistics) Johnson, Brad (Statistics) Guo, Benqi (Mathematics) Li, Gang (Animas Corporation | LifeScan, Inc. | Johnson & Johnson ) | en_US |
| dc.contributor.supervisor | Fu, James C. (Statistics) | en_US |
| dc.date.accessioned | 2012-07-27T16:55:07Z | |
| dc.date.available | 2012-07-27T16:55:07Z | |
| dc.date.issued | 2010-12 | en_US |
| dc.degree.discipline | Statistics | en_US |
| dc.degree.level | Doctor of Philosophy (Ph.D.) | en_US |
| dc.description.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. | en_US |
| dc.description.note | October 2012 | en_US |
| dc.identifier.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. | en_US |
| dc.identifier.uri | http://hdl.handle.net/1993/8123 | |
| dc.language.iso | eng | en_US |
| dc.publisher | Applied Probability Trust - Journal of Applied Probability | en_US |
| dc.rights | open access | en_US |
| dc.subject | boundary crossing probabilities | en_US |
| dc.subject | Brownian motion | en_US |
| dc.subject | first passage time | en_US |
| dc.subject | finite Markov chain imbedding | en_US |
| dc.subject | diffusion processes | en_US |
| dc.subject | absorption probability | en_US |
| dc.subject | transition probability matrices | en_US |
| dc.subject | random walks | en_US |
| dc.title | Linear and non-linear boundary crossing probabilities for Brownian motion and related processes | en_US |
| dc.type | doctoral thesis | en_US |