高阶广义正规变化尾的随机游动的大偏差估计

The Estimation of Large Deviation of Random Walk with High Order General Regular Variation Tails

研究高阶广义正规变化条件下随机游动的大偏差估计.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,得到一个大偏差估计.利用高阶广义正规变化条件的一个等价形式,得到由独立同分布(i.i.d)随机变量生成的随机游动的大偏差Vn(x)=P{Sn>x}的估计.

In this paper the estimation of large deviation of random walk with high order general regular variation condition is studied. We propose the tails of independent and identically distributed （ i. i. d） random variables have high order general regular variation, and then obtain the estimation of the large deviation probabilities for partial sums. We also use a equivalent condition of high order general variation condition, under the equivalent condition we obtain the estimation of Vn（x）=P{Sn〉x}.