SMALL DEVIATION PROBABILITIES OF WEIGHTED SUMS WITH FAST
DECREASING WEIGHTS
Abstract: We examine small deviation probabilities of weighted sums of i.i.d. positive random
variables whose distribution function is regularly varying at zero provided that weights are
decreasing fast enough.
2000 AMS Mathematics Subject Classification: Primary: 60G50; Secondary:
60F99.
Keywords and phrases: Small deviation probabilities, i.i.d. positive random variables,
weighted sums, slowly varying functions, regularly varying functions.