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Max-infinitely divisible and max-stable sample continuous processes
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  • Published: June 1990

Max-infinitely divisible and max-stable sample continuous processes

  • Evarist Giné1,
  • Marjorie G. Hahn2 &
  • Pirooz Vatan3 

Probability Theory and Related Fields volume 87, pages 139–165 (1990)Cite this article

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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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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Connecticut, 06269, Storrs, CT, USA

    Evarist Giné

  2. Department of Mathematics, Tufts University, 02155, Medford, MA, USA

    Marjorie G. Hahn

  3. M.I.T. Branch, P.O. Box 21, 02139, Cambridge, MA, USA

    Pirooz Vatan

Authors
  1. Evarist Giné
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  2. Marjorie G. Hahn
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  3. Pirooz Vatan
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Additional information

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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  • Received: 22 May 1989

  • Revised: 07 May 1990

  • Issue Date: June 1990

  • DOI: https://doi.org/10.1007/BF01198427

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Keywords

  • Banach Space
  • Hull
  • Stochastic Process
  • Probability Theory
  • Convex Hull
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