RATE OF CONVERGENCE AND EXPANSION OF RNYI ENTROPIC CENTRAL LIMIT THEOREM

• 作 者: 孙建强 丁义明
• 机 构: WuhanInstituteofPhysicsandMathematics,WuhanInstituteofPhysicsandMathematics,NationalCenterforMathema
• 出 处: 数学物理学报：B辑英文版
• 发表日期: 2015年1期
• 关键词: 中心极限定理 收敛速度 连续随机变量 熵 渐近式 归一化 总方差 发散 Renyi divergence central limit theorem Edgew
• 基金项目: This work is supported by National Basic Research Program of China （973 Program） （2011CB707802, 2013CB910200） and Natural Science Foundation of China Grant （11126180）.

We obtain the expansion of Rényi divergence of order α(0 < α < 1) between the normalized sum of IID continuous random variables and the Gaussian limit under minimal moment conditions via Edgeworth-type expansion. The rate is faster than that of