On occupation times of stationary excursions
| dc.creator | Kozlova, Marina | |
| dc.creator | Salminen, Paavo | |
| dc.date | 2004-08-13 | |
| dc.date | 2004-08-24 | |
| dc.date.accessioned | 2026-07-07T05:11:15Z | |
| dc.date.available | 2026-07-07T05:11:15Z | |
| dc.description | In this paper excursions of a stationary diffusion in stationary state are studied. In particular, we compute the joint distribution of the occupation times $I^{(+)}_t$ and $I^{(-)}_t$ above and below, respectively, the observed level at time $t$ during an excursion. We consider also the starting time $g_t$ and the ending time $d_t$ of the excursion (straddling $t$) and discuss their relations to the Levy measure of the inverse local time. It is seen that the pairs $(I^{(+)}_t, I^{(-)}_t)$ and $(t-g_t, d_t-t)$ are identically distributed. Moreover, conditionally on $I^{(+)}_t + I^{(-)}_t =v$, the variables $I^{(+)}_t$ and $I^{(-)}_t$ are uniformly distributed on $(0,v)$. Using the theory of the Palm measures, we derive an analoguous result for excursion bridges. | |
| dc.description | 32 pages; extended abstract | |
| dc.identifier | https://arxiv.org/abs/math/0408178 | |
| dc.identifier | http://arxiv.org/abs/math/0408178 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72180 | |
| dc.subject | Probability | |
| dc.subject | 60J60, 60G10 | |
| dc.title | On occupation times of stationary excursions | |
| dc.type | text |