Estimation of the probability a Brownian bridge crosses a concave boundary / by Fan Yang.
| Author/creator | Yang, Fan |
| Other author | Carolan, Christopher (Christopher A.) |
| Other author | East Carolina University. Department of Mathematics. |
| Format | Theses and dissertations |
| Publication Info | [Greenville, N.C.] : East Carolina University, 2010. |
| Description | 46 pages : illustrations (color), digital, PDF file |
| Supplemental Content | Access via ScholarShip |
| Subjects |
| Summary | This thesis studies a new method to estimate the probability that a Brownian bridge crosses a concave boundary. We show that a Brownian bridge crosses a concave boundary if and only if its least concave majorant crosses said concave boundary. As such, we can equivalently simulate the least concave majorant of a Brownian bridge in order to estimate the probability that a Brownian bridge crosses a concave boundary. We apply these theoretical results to the problem of estimating joint confidence intervals for a true CDF at every point. We compare this method to a traditional method for estimating joint confidence intervals for the true CDF at every point which is based upon the limiting distribution of what is often called the Kolmogorov-Smirnov distance, the sup-norm distance between the empirical and true CDFs. We indicate the disadvantages of the traditional approach and demonstrate how our approach addresses these weaknesses. |
| General note | Presented to the faculty of the Department of Mathematics. |
| General note | Advisor: Christopher Carolan. |
| General note | Title from PDF t.p. (viewed Nov. 3, 2010). |
| Dissertation note | M.A. East Carolina University 2010. |
| Bibliography note | Includes bibliographical references. |
| Technical details | System requirements: Adobe Reader. |
| Technical details | Mode of access: World Wide Web. |
Availability
| Library | Location | Call Number | Status | Item Actions |
|---|---|---|---|---|
| Electronic Resources | Access Content Online | ✔ Available |