一类非标准随机游动的尾分布的渐近表达式

The Asymptotic Behavior of the Tail Probabilities for a Non-standard Random Walk

设{Y1i,i=1,2,L}为独立同分布随机变量,{Y2i,i=1,2,L}为独立同分布随机变量,它们都支撑在[0,∞)上,且它们的分布函数分别为F,G,称Sn,n=1,2L为非标准随机游动,若令S2n=Y11+Y21+L+Y1n+Y2n,S2n+1=Y11+Y21+LY1n+Y2n+Y1,n+1,S0=0.本文研究了当F,G∈S,S(γ),G∈S时,随机游动变量部分和S的尾分布P(g>x)的渐近表达式.

Let {Y1i,i= 1,2,L}be a sequence of independent and identiacally distributed random variables, and { Y2i, i = 1, 2, L } be a sequence of independent and identiacally distributed random variables. They are both supported on[0,∞） . F,G are their distributed functions respectively. We callSn,n≥1 Nonstandard Random Walk, whereS2n=Y11＋Y21＋L＋Y1n＋Y2n,S2n＋1=Y11＋Y21＋LY1n＋Y2n＋Y1,n＋1,S0=0. This paper investigates the asymptotic behavior of the tail probabilities P（g〉x） of the quantitySn=n↑∑↓i=1 Xifor F,G∈S,S（γ）. G∈S .