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Semistable distributions as marginals of operator stable laws

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  • Kern, P.
  • Scheffler, H.-P.

Abstract

An example of Meerschaert (1990) shows that univariate marginals of an operator stable distribution are not necessarily stable distributions, but turned out to be semistable as shown by Meerschaert and Scheffler (1999). We characterize all semistable distributions that can appear as an univariate marginal of an operator stable law in terms of the spectral measure.

Suggested Citation

  • Kern, P. & Scheffler, H.-P., 2025. "Semistable distributions as marginals of operator stable laws," Statistics & Probability Letters, Elsevier, vol. 226(C).
    • Handle: RePEc:eee:stapro:v:226:y:2025:i:c:s0167715225001038
    DOI: 10.1016/j.spl.2025.110458
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    References listed on IDEAS

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    1. Cohen, Serge & Meerschaert, Mark M. & Rosinski, Jan, 2010. "Modeling and simulation with operator scaling," Stochastic Processes and their Applications, Elsevier, vol. 120(12), pages 2390-2411, December.
    2. Makoto Maejima & Riddhi Shah, 2006. "Moments and Projections of Semistable Probability Measures on p-adic Vector Spaces," Journal of Theoretical Probability, Springer, vol. 19(2), pages 447-459, June.
    3. 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.
    4. Makoto Maejima & Gennady Samorodnitsky, 1999. "Certain Probabilistic Aspects of Semistable Laws," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(3), pages 449-462, September.
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