Journal of Theoretical Probability

, Volume 10, Issue 1, pp 73–86

The Equivalence of Ergodicity and Weak Mixing for Infinitely Divisible Processes

  • Jan Rosiński
  • Tomasz Żak

DOI: 10.1023/A:1022690230759

Cite this article as:
Rosiński, J. & Żak, T. Journal of Theoretical Probability (1997) 10: 73. doi:10.1023/A:1022690230759


The equivalence of ergodicity and weak mixing for general infinitely divisible processes is proven. Using this result and [9], simple conditions for ergodicity of infinitely divisible processes are derived. The notion of codifference for infinitely divisible processes is investigated, it plays the crucial role in the proofs but it may be also of independent interest.

Stationary process ergodicity weak mixing infinitely divisible process 

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • Jan Rosiński
    • 1
  • Tomasz Żak
  1. 1.Department of MathematicsUniversity of TennesseeKnoxville

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