We find a universal norming sequence in strong limit theorems for increments of sums of i.i.d. random variables with finite first moments and finite second moments of positive parts. Under various one-sided moment conditions our universal theorems imply the following results for sums and their increments: the strong law of large numbers, the law of the iterated logarithm, the Erdős-Rényi law of large numbers, the Shepp law, one-sided versions of the Csörgő-Révész strong approximation laws. We derive new results for random variables from domains of attraction of a normal law and asymmetric stable laws with index αЄ(1,2).
DEHEUVELS, P. and DEVROYE, L., Limit laws of Erdős-Rényi-Shepp type, Ann. Probab.15 (1987), 1363-1386. MR88f:60055
'Limit laws of Erdős-Rényi-Shepp type' () 15Ann. Probab.: 1363-1386.
Limit laws of Erdős-Rényi-Shepp typeAnn. Probab.1513631386)| false
PETROV, V.V., Limit theorems of probability theory. Sequences of independent random variables, Oxford Studies in Probability, 4, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1995. MR96h:60048
Limit theorems of probability theory. Sequences of independent random variables, ().
Limit theorems of probability theory. Sequences of independent random variables4)| false