CENTRAL LIMIT THEOREM FOR RÉNYI DIVERGENCE OF INFINITEORDER

• 成果类型: Article
• 署名作者: Bobkov, Sergey G.; Goetze, Friedrich
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; University of Bielefeld
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/24-AOP1711
• 发表日期: 2025
• 页码: 453-477
• 关键词: renyi divergence; inequalities; MONOTONICITY; CONVERGENCE; entropy

摘要

For normalized sumsZnof i.i.d. random variables, we explore necessaryand sufficient conditions, which guarantee the normal approximation withrespect to the R & eacute;nyi divergence of infinite order. In terms of densitiespnofZn, this is a strengthened variant of the local limit theorem taking the formsupx(pn(x)-phi(x))/phi(x)-> 0asn ->infinity