On the path structure of a semimartingale arising from monotone probability theory
| dc.creator | Belton, Alexander C. R. | |
| dc.date | 2007-09-24 | |
| dc.date | 2008-05-22 | |
| dc.date.accessioned | 2026-07-07T09:40:03Z | |
| dc.date.available | 2026-07-07T09:40:03Z | |
| dc.description | Let $X$ be the unique normal martingale such that $X_0=0$ and \[\mathrm{d}[X]_t=(1-t-X_{t-}) \mathrm{d}X_t+\mathrm{d}t\] and let $Y_t:=X_t+t$ for all $t\geq 0$; the semimartingale $Y$ arises in quantum probability, where it is the monotone-independent analogue of the Poisson process. The trajectories of $Y$ are examined and various probabilistic properties are derived; in particular, the level set $\{t\geq 0\dvt Y_t=1\}$ is shown to be non-empty, compact, perfect and of zero Lebesgue measure. The local times of $Y$ are found to be trivial except for that at level 1; consequently, the jumps of $Y$ are not locally summable. | |
| dc.description | Published in at http://dx.doi.org/10.1214/07-AIHP116 the Annales de l'Institut Henri Poincaré - Probabilités et Statistiques (http://www.imstat.org/aihp/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/0709.3788 | |
| dc.identifier | http://arxiv.org/abs/0709.3788 | |
| dc.identifier | Annales de l'Institut Henri Poincaré - Probabilités et Statistiques 2008, Vol. 44, No. 2, 258-279 | |
| dc.identifier | doi:10.1214/07-AIHP116 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/161364 | |
| dc.subject | Probability | |
| dc.subject | 60G44 (Primary) | |
| dc.title | On the path structure of a semimartingale arising from monotone probability theory | |
| dc.type | text |