Uniform bound for asymptotic normality of discounted m-dependent random variables using Heinrich's method

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• 作者：J. Sunklodas
• 关键词：discounted central limit theorem ; m ; dependent random variables ; Heinrich’ ; s method
• 刊名：Lithuanian Mathematical Journal
• 出版时间：October, 2009
• 出版年：2009
• 期刊代码：35_03631672
• 类别：cp
• 卷：49
• 期：4
• 页码：464-470
• 数据来源：sp

摘要

We estimate the difference | F_Zv(x) - F(x) | \left| {{F_{{Z_v}}}(x) - \Phi (x)} \right| , where F_Zv(x) {F_{{Z_v}}}(x) is the distribution function of normalized series Z _v = B −1 _v Σ∞ _j=0 v j X _j with B 2 _v = \mathbb E \mathbb {E} (Σ∞ _j=0 v j X _j ) > 0 and the discount factor v, 0 < v < 1; X ₀,X ₁,X ₂,… is a sequence of m-dependent random variables, and Φ(x) is the standard normal distribution function. In a particular case, the obtained upper bound is of order O((1−v)1/2).