The Poisson storm process Extremal coefficients and simulation

Description

The Poisson storm process Extremal coefficients and simulation C. Lantuejoul1, J.N. Bacro2 and L. Bel3 1MinesParisTech 2Universite de Montpellier II 3AgroParisTech 1

• basic ingredients


• poisson point


• process


• gaussian storm


• exist between extremal


• storm process

Sujets

• Process

Informations

• Publié par: profil-urra-2012
• Nombre de lectures: 40
• Langue: English

Extrait

ThePoissonstormprocess Extremalcoefficientsandsimulation C.Lantue ´ joul 1 ,J.N.Bacro 2 andL.Bel 3 1 MinesParisTech 2 Universite´deMontpellierII 3 AgroParisTech 1

Stormprocess IntroducedbySmith(1990)andgeneralizedbySchlather(2002),thestorm processisaprototypeofmax-stableprocesseswithunitFre´chetmargins: ´³ α F(z)=exp−z>0 z Basicingredients: –ΠhomogenousPoissonpointprocess(intensityµ)inIR d ×IR + ; ¡¢ –Y x,t ,x∈IR d ,t∈IR + independentcopiesofarandomfunctionY, definedinIR d ,positiveandintegrable. Definition: Z(s)=sup Y x,t (s−x) (x,t)∈Π t d RI∈s 2

Gaussianmrotsprocesses Y(s)=epx µ ta − sxi |s| 2 2 σ ¶ differentscales 3