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math.PR2026
The Berry--Esseen Estimate in the Free Central Limit Theorem
Makoto Maejima, Noriyoshi Sakuma
We consider sums of freely independent self-adjoint random variables that are not necessarily identically distributed. Let denote the distribution of the th summand. We as…
math.PR2026
Scaling limit theorem for mixed free and Boolean convolution powers
Hao-Wei Huang, Noriyoshi Sakuma, Pei-Lun Tseng +1
We prove a scaling limit theorem for a double sequence of probability measures involving additive free convolution and additive Boolean convolution . Let be…
math.PR2026
Modified ruin probability for a Cramér-Lundberg model driven by a compound mixed Poisson process
Noriyoshi Sakuma, Momoka Tashiro
We study modified ruin probabilities in a Cramér-Lundberg model driven by a compound mixed Poisson process. In the heavy-tailed regime, if the integrated claim-size distribution is…