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Regular conditional distributions of continuous max-infinitely divisible random fields

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Regular conditional distributions of continuous max-infinitely divisible random fields
2.	Creator	Author's name, affiliation, country	Clément Dombry; Université de Poitiers; France
2.	Creator	Author's name, affiliation, country	Frédéric Eyi-Minko; Université de Poitiers; France
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	max-infinitely divisible process; max-stable process; regular conditional distribution; point process representation
3.	Subject	Subject classification	60G70; 60G25
4.	Description	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-stable (or max-infinitely divisible) process $\{\eta(t)\}_{t\in T}$ given observations $\{\eta(t_i)=y_i,\ 1\leq i\leq k\}$. Our starting point is the point process representation of max-infinitely divisible processes by Giné, Hahn and Vatan (1990). We carefully analyze the structure of the underlying point process, introduce the notions of extremal function, sub-extremal function and hitting scenario 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. This formula extends a recent result by Wang and Stoev (2011) dealing with the case of spectrally discrete max-stable random fields. This paper offers new tools and perspective or prediction in extreme value theory together with numerous potential applications.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2013-01-13
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/1991
10.	Identifier	Digital Object Identifier	10.1214/EJP.v18-1991
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 18
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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