Limit theorems in free probability theory.: I

• 成果类型: Article
• 署名作者: Chistyakov, G. P.; Goetze, F.
• 署名单位: National Academy of Sciences Ukraine; B. Verkin Institute for Low Temperature Physics & Engineering of the National Academy of Sciences of Ukraine; University of Bielefeld
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117907000000051
• 发表日期: 2008
• 页码: 54-90
• 关键词: free convolution; Levy processes; large numbers; LAW; multiplication; REGULARITY; atoms

摘要

Based on an analytical approach to the definition of additive free convolution on probability measures on the real line, we prove free analogues of limit theorems for sums for nonidentically distributed random variables in classical probability theory.