000221994 001__ 221994
000221994 005__ 20181203024405.0
000221994 0247_ $$2doi$$a10.1214/16-Ejp1112
000221994 022__ $$a1083-6489
000221994 02470 $$2ISI$$a000378990000014
000221994 037__ $$aARTICLE
000221994 245__ $$aA Levy-derived process seen from its supremum and max-stable processes
000221994 260__ $$bUniv Washington, Dept Mathematics$$c2016$$aSeattle
000221994 269__ $$a2016
000221994 300__ $$a19
000221994 336__ $$aJournal Articles
000221994 520__ $$aWe consider a process Z on the real line composed from a Levy process and its exponentially tilted version killed with arbitrary rates and give an expression for the joint law of the supremum (Z) over bar, its time T, and the process Z(T + center dot) - (Z) over bar. This expression is in terms of the laws of the original and the tilted Levy processes conditioned to stay negative and positive respectively. The result is used to derive a new representation of stationary particle systems driven by Levy processes. In particular, this implies that a max-stable process arising from Levy processes admits a mixed moving maxima representation with spectral functions given by the conditioned Levy processes.
000221994 6531_ $$aconditionally positive process
000221994 6531_ $$aIto's excursion theory
000221994 6531_ $$amixed moving maxima representation
000221994 6531_ $$astationary particle system
000221994 6531_ $$aKuznetsov measure
000221994 700__ $$0246548$$g224237$$uEcole Polytech Fed Lausanne, CH-1015 Lausanne, Switzerland$$aEngelke, Sebastian
000221994 700__ $$aIvanovs, Jevgenijs
000221994 773__ $$j21$$tElectronic Journal Of Probability$$q14
000221994 909C0 $$xU10124$$0252136$$pSTAT
000221994 909CO $$pSB$$particle$$ooai:infoscience.tind.io:221994
000221994 917Z8 $$x111184
000221994 937__ $$aEPFL-ARTICLE-221994
000221994 973__ $$rREVIEWED$$sPUBLISHED$$aEPFL
000221994 980__ $$aARTICLE