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Random integral representations for classes of limit distributions similar to levy class L 0
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  • Published: July 1988

Random integral representations for classes of limit distributions similar to levy class L 0

  • Zbigniew J. Jurek1 nAff2 

Probability Theory and Related Fields volume 78, pages 473–490 (1988)Cite this article

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  • 23 Citations

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Summary

For a bounded linear operator Q, on a Banach space E, and a real number β, there are introduced classes, U β(Q), of some limit distributions such that U O(I coincides with the Lévy class L 0. Elements from U β(Q are characterized in terms of convolution equations and as probability distributions of some random integral functionals. The continuity and fixed points of this random mapping is studied. It is shown that fixed points coincide with the class of Q-stable measures.

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Author information

Author notes
  1. Zbigniew J. Jurek

    Present address: Institute of Mathematics, University of Wroclaw, PL-50-384, Wroclaw, Poland

Authors and Affiliations

  1. Center for Stochastic Processes, University of North Carolina, 27514, Chapel Hill, NC, USA

    Zbigniew J. Jurek

Authors
  1. Zbigniew J. Jurek
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Additional information

This work partially supported by AFOSR Grant No. F49620 82 C 0009

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Cite this article

Jurek, Z.J. Random integral representations for classes of limit distributions similar to levy class L 0 . Probab. Th. Rel. Fields 78, 473–490 (1988). https://doi.org/10.1007/BF00334208

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  • Received: 12 October 1985

  • Revised: 28 December 1987

  • Issue Date: July 1988

  • DOI: https://doi.org/10.1007/BF00334208

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Keywords

  • Probability Distribution
  • Banach Space
  • Real Number
  • Stochastic Process
  • Convolution
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