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Random integral representations for free-infinitely divisible and tempered stable distributions

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  • Jurek, Zbigniew J.

Abstract

There are given sufficient conditions under which mixtures of dilations of Lévy spectral measures, on a Hilbert space, are Lévy measures again. We introduce some random integrals with respect to infinite-dimensional Lévy processes, which in turn give some integral mappings. New classes (convolution semigroups) are introduced. One of them gives an unexpected relation between the free (Voiculescu) and the classical Lévy-Khintchine formulae while the second one coincides with tempered stable measures (Mantegna and Stanley) arisen in statistical physics.

Suggested Citation

  • Jurek, Zbigniew J., 2007. "Random integral representations for free-infinitely divisible and tempered stable distributions," Statistics & Probability Letters, Elsevier, vol. 77(4), pages 417-425, February.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:4:p:417-425
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    Cited by:

    1. Jurek, Zbigniew J., 2018. "Remarks on compositions of some random integral mappings," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 277-282.
    2. Michael Grabchak, 2015. "Inversions of Lévy Measures and the Relation Between Long and Short Time Behavior of Lévy Processes," Journal of Theoretical Probability, Springer, vol. 28(1), pages 184-197, March.

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