Small deviations of series of weighted i.i.d. non-negative random variables with a positive mass at the origin
We study the small deviations of [summation operator]j>=1[lambda]jXj and supj>=1[lambda]jXj, where {Xj} are i.i.d. non-negative random variables and 1/[lambda]j tends to [infinity] faster than any power of j. The most interesting conclusions hold if .