2007/07/23 by Jiun-Chau Wang, Wang, Jiun-Chau · 1 citation
Economics, Econometrics and Finance · #46L53 #46L54 #FOS: Mathematics #Operator Algebras (math.OA) #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.0707.3401
openalex publication_date 2007/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the distributional behavior for products, and for sums of boolean independent random variables in an infinitesimal triangular array. We show that the limit laws of boolean convolutions are determined by the limit laws of free convolutions, and vice versa. We further use these results to show several connections between the limiting distributional behavior of classical convolutions and that of boolean convolutions. The proof of our results is based on the analytical apparatus developed for free convolutions.