Extremal shot noises, heavy tails and max-stable random fields

نویسنده

  • Clément Dombry
چکیده

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 R × (0,+∞) with intensity λdxG(dm) and h : R → [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. AMS Subject classification: Primary: 60F17, 60G70; Secondary: 60G55, 60G60.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

January 22, 2013 MEASURES OF SERIAL EXTREMAL DEPENDENCE AND THEIR ESTIMATION

The goal of this paper is two-fold: 1. We review classical and recent measures of serial extremal dependence in a strictly stationary time series as well as their estimation. 2. We discuss recent concepts of heavy-tailed time series, including regular variation and max-stable processes. Serial extremal dependence is typically characterized by clusters of exceedances of high thresholds in the se...

متن کامل

A note on bounds and monotonicity of spatial stationary Cox shot noises

We consider shot-noise processes and max-shot-noise processes driven by spatial stationary Cox (doubly stochastic Poisson) processes. We derive the upper and lower bounds of them in terms of the increasing convex order, which is known as the order relation to compare the variability of random variables. Furthermore, under some regularity assumption of the random intensity fields of Cox processe...

متن کامل

On Scaling Limits of Power Law Shot-noise Fields

This article studies the scaling limit of a class of shot-noise fields defined on an independently marked stationary Poisson point process and with a power law response function. Under appropriate conditions, it is shown that the shot-noise field can be scaled suitably to have a non degenerate α-stable limit, as the intensity of the underlying point process goes to infinity. More precisely, fin...

متن کامل

On the max-semistable limit of maxima of stationary sequences with missing values

Let {Xn} be a stationary sequence with marginal distribution in the domain of attraction of a max-semistable distribution. This includes all distributions in the domain of attraction of any max-stable distribution and also other distributions like some integervalued distributions with exponential type tails such as the Negative Binomial case. We consider the effect of missing values on the dist...

متن کامل

On Max-sum Equivalence and Convolution Closure of Heavy-tailed Distributions and Their Applications

In this paper, we discuss max-sum equivalence and convolution closure of heavy-tailed distributions. We generalize the well-known max-sum equivalence and convolution closure in the class of regular variation to two larger classes of heavy-tailed distributions. As applications of these results, we study asymptotic behaviour of the tails of compound geometric convolutions, the ruin probability in...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2016