2009/08/28 by Clément Dombry, Dombry, Clément
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR
paper · pdf · doi:10.48550/arxiv.0908.4221
31 p
openalex publication_date 2009/08/28 · arxiv created 2010/05/31 · arxiv updated 2010/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the extremal shot noise defined by M(y)=sup\mh(y-x);(x,m)∈Φ\, where Φ is a Poisson point process on \bbRd× (0,+∞) with intensity λdxG(dm) and h:\bbRd→ [0,+∞] is a measurable function. Extremal shot noises naturally appear in extreme value theory as a model for spatial extremes and serve as basic models for annual maxima of rainfall or for coverage field in telecommunications. In this work, we examine their properties such as boundedness, regularity and ergodicity. Connections with max-stable random fields are established: we prove a limit theorem when the distribution G is heavy-tailed and the intensity of points λ goes to infinity. We use a point process approach strongly connected to the Peak Over Threshold method used in extreme value theory. Properties of the limit max-stable random fields are also investigated.