Limit theorems for Lévy flights on a 1D Lévy random medium

dc.bibliographicCitation.firstPage57eng
dc.bibliographicCitation.journalTitleElectronic journal of probability : EJPeng
dc.bibliographicCitation.volume26eng
dc.contributor.authorStivanello, Samuele
dc.contributor.authorBet, Gianmarco
dc.contributor.authorBianchi, Alessandra
dc.contributor.authorLenci, Marco
dc.contributor.authorMagnanini, Elena
dc.date.accessioned2022-06-21T05:49:45Z
dc.date.available2022-06-21T05:49:45Z
dc.date.issued2021
dc.description.abstractWe study a random walk on a point process given by an ordered array of points (ωk,k∈Z) on the real line. The distances ωk+1−ωk are i.i.d. random variables in the domain of attraction of a β-stable law, with β∈(0,1)∪(1,2). The random walk has i.i.d. jumps such that the transition probabilities between ωk and ωℓ depend on ℓ−k and are given by the distribution of a Z-valued random variable in the domain of attraction of an α-stable law, with α∈(0,1)∪(1,2). Since the defining variables, for both the random walk and the point process, are heavy-tailed, we speak of a Lévy flight on a Lévy random medium. For all combinations of the parameters α and β, we prove the annealed functional limit theorem for the suitably rescaled process, relative to the optimal Skorokhod topology in each case. When the limit process is not càdlàg, we prove convergence of the finite-dimensional distributions. When the limit process is deterministic, we also prove a limit theorem for the fluctuations, again relative to the optimal Skorokhod topology.eng
dc.description.versionpublishedVersioneng
dc.identifier.urihttps://oa.tib.eu/renate/handle/123456789/9080
dc.identifier.urihttps://doi.org/10.34657/8118
dc.language.isoengeng
dc.publisher[Madralin] : EMIS ELibEMSeng
dc.relation.doihttps://doi.org/10.1214/21-EJP626
dc.relation.essn1083-6489
dc.rights.licenseCC BY 4.0 Unportedeng
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/eng
dc.subject.ddc510eng
dc.subject.otherAnomalous diffusioneng
dc.subject.otherLévy flightseng
dc.subject.otherLévy random mediumeng
dc.subject.otherRandom walk on point processeng
dc.subject.otherStable distribu-tionseng
dc.subject.otherStable processeseng
dc.titleLimit theorems for Lévy flights on a 1D Lévy random mediumeng
dc.typeArticleeng
dc.typeTexteng
tib.accessRightsopenAccesseng
wgl.contributorWIASeng
wgl.subjectMathematikeng
wgl.typeZeitschriftenartikeleng
Files
Original bundle
Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
Limit_theorems_for.pdf
Size:
585.07 KB
Format:
Adobe Portable Document Format
Description:
Collections