Convergence of dependent walks in a random scenery to fBm-local time fractional stable motions
| dc.creator | Cohen, Serge | |
| dc.creator | Dombry, Clément | |
| dc.date | 2008-05-20 | |
| dc.date.accessioned | 2026-07-07T12:19:05Z | |
| dc.date.available | 2026-07-07T12:19:05Z | |
| dc.description | It is classical to approximate the distribution of fractional Brownian motion by a renormalized sum $ S_n $ of dependent Gaussian random variables. In this paper we consider such a walk $ Z_n $ that collects random rewards $ ξ_j $ for $ j \in \mathbb Z,$ when the ceiling of the walk $ S_n $ is located at $ j.$ The random reward (or scenery) $ ξ_j $ is independent of the walk and with heavy tail. We show the convergence of the sum of independent copies of $ Z_n$ suitably renormalized to a stable motion with integral representation, whose kernel is the local time of a fractional Brownian motion (fBm). This work extends a previous work where the random walk $ S_n$ had independent increments limits. | |
| dc.identifier | https://arxiv.org/abs/0805.3054 | |
| dc.identifier | http://arxiv.org/abs/0805.3054 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/212632 | |
| dc.subject | Probability | |
| dc.subject | 60G18, 60G52, 60F17 | |
| dc.title | Convergence of dependent walks in a random scenery to fBm-local time fractional stable motions | |
| dc.type | text |