Regular conditional distributions of continuous max-infinitely divisible random fields
type: Item
instance of: scholarly article
title: Regular conditional distributions of continuous max-infinitely divisible random fields
zbMATH Open document ID: 1287.60066
author: Frédéric Eyi-Minko
author: Clément Dombry
published in: Electronic Journal of Probability
publication date: 2014-01-17T00:00:00Z
full work available at URL: https://arxiv.org/abs/1109.6492
review text: From the abstract: ``This paper is devoted to the prediction problem in extreme value theory. Our main result is an explicit expression of the regular conditional distribution of a max-stale (or max-infinitely divisible) process \(\left\{ \eta\left( t\right) \right\} _{t\in T}\) withgiven observations \(\left\{ \eta\left( t_{i}\right) =y_{i},1\leq i\leq k\right\} \). [~\dots] We carefully analize the structure of the underlying point process, introduce the notions of extremal functions, sub-extremal functions and hitting scenarios associated to the constraints and derive the associated distributions. This allows us to explicit the conditional distribution as a mixture over all hitting scenarios compatible with the conditioning constraints. [\dots] This paper offers new tools and a perspective for the prediction in extreme value theory together with numerous potential applications.''
reviewed by: Wiesław Dziubdziela
Mathematics Subject Classification ID: 60G70
Mathematics Subject Classification ID: 60G25
zbMATH DE Number: 6247176
zbMATH Keywords: MAX-infinitely divisible process
zbMATH Keywords: MAX-stable process
zbMATH Keywords: regular conditional distribution
zbMATH Keywords: point process representation
MaRDI profile type: Publication
arXiv ID: 1109.6492
DOI: 10.1214/EJP.V18-1991
description: scientific article; zbMATH DE number 6247176