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Probability Theory and Related Fields

, Volume 82, Issue 3, pp 451–487 | Cite as

Spectral representations of infinitely divisible processes

  • Balram S. Rajput
  • Jan Rosinski
Article

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”.

Keywords

Hilbert Space Stochastic Process Probability Theory Statistical Theory Spectral Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Balram S. Rajput
    • 1
  • Jan Rosinski
    • 1
  1. 1.Department of MathematicsUniversity of Tennessee at KnoxvilleKnoxvilleUSA

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