A generalization of Doob's maximal identity
| dc.creator | Nikeghbali, Ashkan | |
| dc.date | 2008-02-10 | |
| dc.date.accessioned | 2026-07-07T09:19:49Z | |
| dc.date.available | 2026-07-07T09:19:49Z | |
| dc.description | In this paper, using martingale techniques, we prove a generalization of Doob's maximal identity in the setting of continuous nonnegative local submartingales $(X_{t})$ of the form: $X_{t}=N_{t}+A_{t}$, where the measure $(dA_{t})$ is carried by the set $\left\{t: X_{t}=0\right\}$. In particular, we give a multiplicative decomposition for the Azéma supermartingale associated with some last passage times related to such processes and we prove that these non-stopping times contain very useful information. As a consequence, we obtain the law of the maximum of a continuous nonnegative local martingale $(M_t)$ which satisfies $M_\infty=ψ(\sup_{t\geq0}M_t)$ for some measurable function $ψ$ as well as the law of the last time this maximum is reached. | |
| dc.identifier | https://arxiv.org/abs/0802.1317 | |
| dc.identifier | http://arxiv.org/abs/0802.1317 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/154531 | |
| dc.subject | Probability | |
| dc.subject | 05C38, 15A15 (Primary); 15A18 (Secondary) | |
| dc.title | A generalization of Doob's maximal identity | |
| dc.type | text |