This thesis is concerned with boundary crossing probabilities and first crossing time densities for stochastic processes. This is a classical problem in probability that goes back to the famous ballot problem (first studied by W. A. Whitworth (1878) and J. Bertrand (1887)) and has numerous applications in diverse areas including mathematical statistics and financial mathematics. Our main objective is the study of approximation methods and control of the resulting approximation error for boundary crossing probabilities where a closed-form solution is unavailable. This leads to the study of bounds for the density of the first crossing time of the boundary, which in turn leads to the derivation of some analytic properties of the densities. This thesis presents a whole suite of closely related new results obtained when working on the outlined research program. (For complete abstract open document).
| Identifer | oai:union.ndltd.org:ADTP/245441 |
| Date | January 2008 |
| Creators | Downes, Andrew Nicholas |
| Source Sets | Australiasian Digital Theses Program |
| Language | English |
| Detected Language | English |
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