【摘要】 设{Xn,n≥1}是同分布正的强混合随机变量序列.利用强混合序列的中心极限定理以及大数定律,在适当的条件下证明了∏nk=1Skn!μn1/(γσn)deN,n→∞,其中Sk=∑ki=1Xi,μ=EX1>0,σ2=VarX1<∞,γ=σμ,σn2=Var1γ∑kn=1kSμk-1,N为标准正态随机变量.更多还原

【Abstract】 Let {Xn,n≥1} be a sequence of strong mixing identically distributed positive random variable,under some suitable conditions,by means of the central limit theorem and the law of large numbers of strong mixing sequence,it is proved that ∏nk=1Skn!μn1/(γσn)deN,n→∞,where Sk=∑ki=1Xi,μ=EX1>0,σ2=Var X1<∞,γ=σμ,σ2n=Var1γ∑nk=1Skkμ-1,and N is a standrad normal random variable.更多还原