Sharp estimate on the supremum of a class of partial sums of small i.i.d. random variables [article]

Peter Major
2014 arXiv   pre-print
We take an L_1-dense class of functions F on a measurable space (X, X) together with a sequence of independent, identically distributed X-space valued random variables ξ_1,...,ξ_n and give a good estimate on the tail distribution of _f∈ F∑_j=1^n f(ξ_j) if the expected values E|f(ξ_1)| are very small for all f∈ F. In a subsequent paper [2] we shall give a sharp bound for the supremum of normalized sums of i.i.d. random variables in a more general case. But that estimate is a consequence of the results in this work.
arXiv:1407.1224v1 fatcat:palzma2dfnbmpjlklvm3ee5tk4