Convergence of dependent walks in a random scenery to fBm-local time fractional stable motions

dc.creatorCohen, Serge
dc.creatorDombry, Clément
dc.date2008-05-20
dc.date.accessioned2026-07-07T12:19:05Z
dc.date.available2026-07-07T12:19:05Z
dc.descriptionIt 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.identifierhttps://arxiv.org/abs/0805.3054
dc.identifierhttp://arxiv.org/abs/0805.3054
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/212632
dc.subjectProbability
dc.subject60G18, 60G52, 60F17
dc.titleConvergence of dependent walks in a random scenery to fBm-local time fractional stable motions
dc.typetext

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