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Spectral representations of infinitely divisible processes
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  • Published: August 1989

Spectral representations of infinitely divisible processes

  • Balram S. Rajput1 &
  • Jan Rosinski1 

Probability Theory and Related Fields volume 82, pages 451–487 (1989)Cite this article

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Summary

The spectral representations for arbitrary discrete parameter infinitely divisible processes as well as for (centered) continuous parameter infinitely divisible processes, which are separable in probability, are obtained. The main tools used for the proofs are (i) a “polar-factorization” of an arbitrary Lévy measure on a separable Hilbert space, and (ii) the Wiener-type stochastic integrals of non-random functions relative to arbitrary “infinitely divisible noise”.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Tennessee at Knoxville, 121 Ayres Hall, 37996-1300, Knoxville, TN, USA

    Balram S. Rajput & Jan Rosinski

Authors
  1. Balram S. Rajput
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  2. Jan Rosinski
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Additional information

The research of both authors was supported partially by the AFSOR Grant No. 87-0136; the second named author was also supported partially by a grant from the University of Tennessee

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Rajput, B.S., Rosinski, J. Spectral representations of infinitely divisible processes. Probab. Th. Rel. Fields 82, 451–487 (1989). https://doi.org/10.1007/BF00339998

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  • Received: 18 March 1987

  • Revised: 12 September 1988

  • Issue Date: August 1989

  • DOI: https://doi.org/10.1007/BF00339998

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Keywords

  • Hilbert Space
  • Stochastic Process
  • Probability Theory
  • Statistical Theory
  • Spectral Representation
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