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Brillinger-mixing point processes need not to be ergodic

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  • Heinrich, Lothar

Abstract

Recently, it has been proved that a stationary Brillinger-mixing point process is mixing (of any order) if its moment measures determine the distribution uniquely. In this paper we construct a family of non-ergodic stationary point processes as mixture of two distinct Brillinger-mixing Neyman–Scott processes having the same moment measures.

Suggested Citation

  • Heinrich, Lothar, 2018. "Brillinger-mixing point processes need not to be ergodic," Statistics & Probability Letters, Elsevier, vol. 138(C), pages 31-35.
    • Handle: RePEc:eee:stapro:v:138:y:2018:i:c:p:31-35
    DOI: 10.1016/j.spl.2018.02.029
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    References listed on IDEAS

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    1. Ivanoff, Gail, 1982. "Central limit theorems for point processes," Stochastic Processes and their Applications, Elsevier, vol. 12(2), pages 171-186, March.
    2. Lothar Heinrich & Stella Klein, 2014. "Central limit theorems for empirical product densities of stationary point processes," Statistical Inference for Stochastic Processes, Springer, vol. 17(2), pages 121-138, July.
    3. Yongtao Guan & Michael Sherman, 2007. "On least squares fitting for stationary spatial point processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(1), pages 31-49, February.
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