Abstract:

Let {Xn,n≥1} be a strictly stationary ρmi
xing sequence of positive random variable, with EX1=μ>0 and Var X1=σ
2<∞. Denote Sn=∑〖DD(〗n〖〗i=1〖DD)〗Xi, Tn=∑〖DD(〗n〖〗i=1〖DD
)〗Si[KG*2]and γ=σ/μ. Using the strong limit theorems of ρmixing seque
nce, under some suitable conditions, we showed that
〖JB((〗∏〖DD(〗n〖〗k=1〖DD)〗〖SX(〗2Tk〖〗k(k+1)μ〖SX)〗〖JB))〗1
/(γσ1〖KF(〗n〖KF)〗)〖FY(〗d〖FY)〗e〖KF(〗10/3〖KF)〗N(n→∞),
where σ21=1+〖SX(〗2〖〗σ2〖SX)〗∑〖DD(〗∞〖〗j=2〖DD)〗Cov(X1
,Xj)>0, N is a standrad normal random variable.[HJ]

Key words: ρ-mixing sequences, product of sums of partial sums, asymptotic distribution, lognormal distribution