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Ergodic properties of random measures on stationary sequences of sets

Author

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  • Gross, Aaron
  • Robertson, James B.

Abstract

We study a class of stationary sequences having spectral representation (M([tau]nA))n[epsilon], where A is a set in a measure space (E, , [mu]), [tau] is an invertible measure-preserving transformation on (E, , [mu]), and M is a random measure on (E, , [mu]). We explore the relationship between the ergodic properties of the sequence and the properties of [tau], and construct examples with various ergodic properties using a stacking method on the half-line [0, [infinity]).

Suggested Citation

  • Gross, Aaron & Robertson, James B., 1993. "Ergodic properties of random measures on stationary sequences of sets," Stochastic Processes and their Applications, Elsevier, vol. 46(2), pages 249-265, June.
    • Handle: RePEc:eee:spapps:v:46:y:1993:i:2:p:249-265
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    Cited by:

    1. Jan Rosiński & Tomasz Żak, 1997. "The Equivalence of Ergodicity and Weak Mixing for Infinitely Divisible Processes," Journal of Theoretical Probability, Springer, vol. 10(1), pages 73-86, January.
    2. Kabluchko, Zakhar & Schlather, Martin, 2010. "Ergodic properties of max-infinitely divisible processes," Stochastic Processes and their Applications, Elsevier, vol. 120(3), pages 281-295, March.

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