Regular conditional distributions of continuous max-infinitely divisible random fields
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.''
scientific article; zbMATH DE number 6247176