The Laws Of The Single Logarithm For Arrays

The paper studies the laws of the single logarithm for arrays of independentrandom variables. The Chung’s type laws of the iterated logarithm for sequences areextended to the laws of the single logarithm for arrays. The necessary and sufficientconditions are obtained. The similar results are also discussed for non-identicallydistributed random variables. The laws of the iterated logarithm for theself-normalized partial sums and the partial sums normalized by the largest absoluteobservation of sequences are extended to the he laws of the single logarithm for arrays.The laws of the iterated logarithm for the R/S statistics of sequences are extended tothe laws of the single logarithm for arrays.