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Regular conditional distributions of continuous max-infinitely divisible random fields. (English) Zbl 1287.60066

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 \(\left\{ \eta\left( t_{i}\right) =y_{i},1\leq i\leq k\right\} \). [ …] 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. […] This paper offers new tools and a perspective for the prediction in extreme value theory together with numerous potential applications.”

MSC:

60G70 Extreme value theory; extremal stochastic processes
60G25 Prediction theory (aspects of stochastic processes)
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