Abstract
The almost sure local central limit theorem is a general result which contains the almost sure global central limit theorem. Let be a sequence of independent and identically distributed (i.i.d.) positive random variables. Under a fairly general condition an universal result in almost sure local limit theorem for the product of some partial sums
is established on the weight
where
and the coefficient of variation
where
MATHEMATICS SUBJECT CLASSIFICATION:
Acknowledgments
The authors are also very grateful to the referees and the editors for their valuable comments and some helpful suggestions that improved the clarity and readability of the paper.