Summary
Conditions for a process ζ on a compact metric spaceS to be simultaneously max-infinitely divisible and sample continuous are obtained. Although they fall short of a complete characterization of such processes, these conditions yield complete descriptions of the sample continuous non-degenerate max-stable processes onS and of the infinitely divisible non-void random compact subsets of a Banach space under the operation of convex hull of unions.
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Partially supported by NSF grant no. DMS-8619411, most of this author's work was carried out at the Centre de Recerca Matemàtica of the Institut d'Estudis Catalann, Barcelona, and at CUNY (College of Staten Island and Graduate Center), and he wishes to acknowledge the hospitality of these institutions.
Partially supported by NSF grant no. DMS-872878
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Giné, E., Hahn, M.G. & Vatan, P. Max-infinitely divisible and max-stable sample continuous processes. Probab. Th. Rel. Fields 87, 139–165 (1990). https://doi.org/10.1007/BF01198427
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DOI: https://doi.org/10.1007/BF01198427