Invariance principles for local times at the supremum of random walks and Lévy processes
| dc.creator | Chaumont, Loïc | |
| dc.creator | Doney, Ron Arthur | |
| dc.date | 2009-03-22 | |
| dc.date.accessioned | 2026-07-07T12:55:33Z | |
| dc.date.available | 2026-07-07T12:55:33Z | |
| dc.description | We prove that when a sequence of Lévy processes $X^{(n)}$ or a normed sequence of random walks $S^{(n)}$ converges a.s. on the Skorokhod space toward a Lévy process $X$, the sequence $L^{(n)}$ of local times at the supremum of $X^{(n)}$ converges uniformly on compact sets in probability toward the local time at the supremum of $X$. A consequence of this result is that the sequence of (quadrivariate) ladder processes (both ascending and descending) converges jointly in law towards the ladder processes of $X$. As an application, we show that in general, the sequence $S^{(n)}$ conditioned to stay positive converges weakly, jointly with its local time at the future minimum, towards the corresponding functional for the limiting process $X$. From this we deduce an invariance principle for the meander which extends known results for the case of attraction to a stable law. | |
| dc.identifier | https://arxiv.org/abs/0903.3705 | |
| dc.identifier | http://arxiv.org/abs/0903.3705 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/224289 | |
| dc.subject | Probability | |
| dc.title | Invariance principles for local times at the supremum of random walks and Lévy processes | |
| dc.type | text |