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About atomless random measures on δ-rings

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  • Kremer, D.
  • Scheffler, H.-P.

Abstract

Independently scattered random measures are usually defined and constructed under the additional condition of being infinitely divisible, a rather strong condition. A more natural condition is the assumption that the random measure has no atoms, that is being atomless. We show that atomless random measures on δ-rings are necessarily infinitely divisible, so infinite divisibility is in fact a quite natural condition.

Suggested Citation

  • Kremer, D. & Scheffler, H.-P., 2020. "About atomless random measures on δ-rings," Statistics & Probability Letters, Elsevier, vol. 164(C).
    • Handle: RePEc:eee:stapro:v:164:y:2020:i:c:s0167715220301085
    DOI: 10.1016/j.spl.2020.108805
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    References listed on IDEAS

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    1. Biermé, Hermine & Meerschaert, Mark M. & Scheffler, Hans-Peter, 2007. "Operator scaling stable random fields," Stochastic Processes and their Applications, Elsevier, vol. 117(3), pages 312-332, March.
    2. Kremer, D. & Scheffler, H.-P., 2019. "Operator-stable and operator-self-similar random fields," Stochastic Processes and their Applications, Elsevier, vol. 129(10), pages 4082-4107.
    3. Li, Yuqiang & Xiao, Yimin, 2011. "Multivariate operator-self-similar random fields," Stochastic Processes and their Applications, Elsevier, vol. 121(6), pages 1178-1200, June.
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