高阶广义正规变化尾随机游动最大值的大偏差概率估计  

The estimation of large deviation probabilities for the maxima of random walk with high order general regular varying tails

作　　者：季海波[1] 王丽[1] 

机构地区：[1]宿迁学院教师教育系,江苏宿迁223800

出　　处：《徐州师范大学学报（自然科学版）》2010年第2期16-19,共4页Journal of Xuzhou Normal University(Natural Science Edition)

基　　金：江苏省高校自然科学基金资助项目(07KJD110093)

摘　　要：研究了高阶广义正规变化条件下随机游动最大值的大偏差估计.假设独立同分布的随机变量的尾分布是高阶广义正规变化函数,得到了一个大偏差估计值.利用洛必达法则得到高阶广义变化条件的一个等价形式,在此等价形式下,得到由独立同分布随机变量生成的随机游动最大值的大偏差估计-Vn(x)=P{-Sn>x}的另外一个估计.The estimation of large deviation probabilities for the maxima of random walk with high order general regular variation is studied. Under the condition that the tails of independent and identically distributed random variables have high order general regular variation, we obtain the estimation of the large deviation probabilities for the maxima of partial sums. With L＇Hospital rule, we also get an equivalent condition of high order general variation under which another estimation of Vn（x）=P{Sn〉x） is given.

关 键 词：大偏差 随机游动 广义正规变化 

分 类 号：O212.62[理学—概率论与数理统计]