Brillinger-mixing point processes need not to be ergodic

Lothar Heinrich

Statistics & Probability Letters, 2018, vol. 138, issue C, 31-35

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.

Keywords: Factorial cumulant measures; Mixing and ergodicity; Poisson cluster processes; Moment problem for point processes (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1016/j.spl.2018.02.029

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