Boolean convolutions and regular variation

Chakraborty, Sukrit ; Hazra, Rajat Subhra (2018) Boolean convolutions and regular variation Latin American Journal of Probability and Mathematical Statistics, 15 (2). pp. 961-991. ISSN 1980-0436

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In this article we study the influence of regularly varying probability measures on additive and multiplicative Boolean convolutions. We introduce the notion of Boolean subexponentiality (for additive Boolean convolution), which extends the notion of classical and free subexponentiality. We show that the distributions with regularly varying tails belong to the class of Boolean subexponential distributions. As an application we also study the behaviour of the Belinschi-Nica map. Breiman's theorem study the classical product convolution between regularly varying measures. We derive an analogous result to Breiman's theorem in case of multiplicative Boolean convolution. In proving these results we exploit the relationship of regular variation with different transforms and their Taylor series expansion.

Item Type:Article
Source:Copyright of this article belongs to ALEA-Latin American Journal of Probability and Mathematical Statistics.
Keywords:Boolean Convolution; Regular Variation; Free Convolution; Subexponential.
ID Code:121055
Deposited On:09 Jul 2021 04:39
Last Modified:09 Jul 2021 04:39

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