Gaussian Distribution Of The Special Weighting And Re-logarithmic Law

The law of the iterated logarithm is a kind of profound result on the limit theory, it make the strong law of large numbers exact . Thelimit theory of law of the iterated logarithm have received more and more attentions, especially about identical independent random variables. But up to now, the studies are only for partial sums and, haven't shown any concern on the special finite partial weight suras .however, the partial sums and partial weight sums not only have the osculating aspects, but also have essential difference between them. So the studies for these play an important role in theoretical and applied setups.The paper consists of two chapters. In the first chapter , theory 1[ 1 ] mainly by using the method of the law of the iterated logarithm with finite partial sum in Wiener process proves Hartman-Wintner [ 1 ] law of the iterated logarithm for special finite partial weight sums. Let{Xn;n > 1} be mutually identically independent random variablesdistributed according to the normal distribution , {Sn,n> 1} be finitepartial sum series, the purpose of this paper is to investigate law of the iterated logarithm type results for special finite partial weightsum series {Sn,n> 1} , we assume thatSn=a1Sn+a2(S2n-Sn) + a3(S3n-S2n) + ...+ ad(Sdn-S(d-1)n) In the second chapter, theory 2 by using the method of literature [8] , weextend Hartman-Wintner law of iterated logarithm on the gauss distribution .we substitute negative correspond for independent. It extends the corresponding results in Gauss distribution.