Solution of Deny convolution equation restricted to a halfr, R. A.: A functional law of the iterated logarithm for distributions in the domain of partial attraction of the normal distribution
The main result is: partial sums of i.i.d. r.v. when suitably normed and centred \((S_ n-a_ n)/B_ n\) are in the domain of partial attraction of the normal distribution iff the set of almost sure limit points of the random polygon as a sequence in C[0,1] or of the partial sum process \((S_{[nt]}-a_{[nt]})/B_ n\) as a sequence in D[0,1], equals to the unit ball of absolutely continuous functions in \(L_ 2\) metric. It is proved that the same statement holds true after removing a fixed number of terms of largest modulus from \(S_ n\).
scientific article; zbMATH DE number 4044836