On maxima and ladder processes for a dense class of Levy processes
| dc.creator | Pistorius, M. R. | |
| dc.date | 2005-02-09 | |
| dc.date.accessioned | 2026-07-07T05:16:50Z | |
| dc.date.available | 2026-07-07T05:16:50Z | |
| dc.description | Consider the problem to explicitly calculate the law of the first passage time T(a) of a general Levy process Z above a positive level a. In this paper it is shown that the law of T(a) can be approximated arbitrarily closely by the laws of T^n(a), the corresponding first passages time for X^n, where (X^n)_n is a sequence of Levy processes whose positive jumps follow a phase-type distribution. Subsequently, explicit expressions are derived for the laws of T^n(a) and the upward ladder process of X^n. The derivation is based on an embedding of X^n into a class of Markov additive processes and on the solution of the fundamental (matrix) Wiener-Hopf factorisation for this class. This Wiener-Hopf factorisation can be computed explicitly by solving iteratively a certain fixed point equation. It is shown that, typically, this iteration converges geometrically fast. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/math/0502192 | |
| dc.identifier | http://arxiv.org/abs/math/0502192 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74137 | |
| dc.subject | Probability | |
| dc.subject | 60G51; 60K15; 60J25 | |
| dc.title | On maxima and ladder processes for a dense class of Levy processes | |
| dc.type | text |