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Random capacities and their distributions
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  • Published: September 1986

Random capacities and their distributions

  • Tommy Norberg1 

Probability Theory and Related Fields volume 73, pages 281–297 (1986)Cite this article

Summary

We formalize the notion of an increasing and outer continuous random process, indexed by a class of compact sets, that maps the empty set on zero. Existence and convergence theorems for distributions of such processes are proved. These results generalize or are similar to those known in the special cases of random measures, random (closed) sets and random (upper) semicontinuous functions. For the latter processes infinite divisibility under the maximum is introduced and characterized. Our result generalizes known characterizations of infinite divisibility for random sets and max-infinite divisibility for random vectors. Also discussed is the convergence in distribution of the row-vise maxima of a null-array of random semicontinuous functions.

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Authors and Affiliations

  1. Department of Mathematics, The University of Göteborg, S-412 96, Göteborg, Sweden

    Tommy Norberg

Authors
  1. Tommy Norberg
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Research supported by the Swedish Natural Science Research Council

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Norberg, T. Random capacities and their distributions. Probab. Th. Rel. Fields 73, 281–297 (1986). https://doi.org/10.1007/BF00339941

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  • Received: 23 March 1984

  • Revised: 17 June 1985

  • Issue Date: September 1986

  • DOI: https://doi.org/10.1007/BF00339941

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Keywords

  • Stochastic Process
  • Probability Theory
  • Statistical Theory
  • Random Process
  • Random Vector
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