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

Zbigniew J. Jurek

Statistics & Probability Letters, 2007, vol. 77, issue 4, 417-425

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.

Keywords: Infinite; divisible; measure; Lévy; spectral; measure; [lambda]-Mixtures; Lévy-Khintchine; formula; Lévy; process; Stable; measures; Hilbert; and; Banach; spaces; Free-infinite; divisibility; Tempered; stable; measures (search for similar items in EconPapers)
Date: 2007
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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