Almost Sure Central Limit Theorem For Self-normalized Products Of The Some Partial Sums Of ρ~--mixing Sequences

Let {X,Xn}n∈N be a strictly stationary ρ--mixing sequence of positive random variables,under the suitable conditions,we get the almost sure cen-tral limit theorem for the products of the some partial sums(?)where β>0 is a constant,andE(X)= μ,(?)The Chapter 1,introduces the research progress of the almost sure cen-tral limit theorem at home and abroad,and gives a brief description of the main work of this paper.The Chapter 2,as the preparatory knowledge,introduces the basic properties of the ρ--mixing random variable sequence and several impor-tant inequalities used in this paper.The Chapter 3,by the properties of the ρ--mixing sequence,moment inequality,Toeplitz lemma,Cr inequality,Holder inequality,Markov in-equality,get the almost sure central limit theorem for self-normalized prod-ucts of the some partial sums of ρ--mixing sequences.