Asymptotic expansions in the CLT in free probability

• 成果类型: Article
• 署名作者: Chistyakov, G. P.; Goetze, F.
• 署名单位: University of Bielefeld; National Academy of Sciences Ukraine; B. Verkin Institute for Low Temperature Physics & Engineering of the National Academy of Sciences of Ukraine
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-012-0451-2
• 发表日期: 2013
• 页码: 107-156
• 关键词: limit-theorems; free convolution

摘要

We prove Edgeworth type expansions for distribution functions of sums of free random variables under minimal moment conditions. The proofs are based on the analytic definition of free convolution.