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Finite thinning-selfdecomposable point processes

Author

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  • Davydov, Michel
  • Zuyev, Sergei

Abstract

Thinning-selfdecomposable point processes arise as a limit in the thinning-superposition schemes of independent but not necessarily identically distributed point processes and, as such, they constitute a strict subclass of infinitely divisible point processes. At the same time they are strictly larger than the class of discrete α-stable point processes which are the limits of a scaled superposition of independent identically distributed processes. We give a series representation for finite thinning-selfdecomposable point processes which can be viewed as an analogue of an integral representation of selfdecomposable (or class L) random variables.

Suggested Citation

  • Davydov, Michel & Zuyev, Sergei, 2019. "Finite thinning-selfdecomposable point processes," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 132-138.
    • Handle: RePEc:eee:stapro:v:146:y:2019:i:c:p:132-138
    DOI: 10.1016/j.spl.2018.11.010
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