Limit Theorems for Additive Conditionally Free Convolution

Wang, Jiun-Chau

Canadian journal of mathematics, Tome 63 (2011) no. 1, pp. 222-240

Résumé

In this paper we determine the limiting distributional behavior for sums of infinitesimal conditionally free random variables. We show that the weak convergence of classical convolution and that of conditionally free convolution are equivalent for measures in an infinitesimal triangular array, where the measures may have unbounded support. Moreover, we use these limit theorems to study the conditionally free infinite divisibility. These results are obtained by complex analytic methods without reference to the combinatorics of $\text{c}$ -free convolution.

Détail

DOI : 10.4153/CJM-2010-075-4

Mots-clés : 46L53, 60F05, additive c-free convolution, limit theorems, infinitesimal arrays

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