For censored sums of regularly varying random variables, the paper derives uniform large-deviation asymptotics for all threshold values of order the cap, with explicit formulas near and between multiples of the cap.
An extension of the concept of slowly varying function with applications to large deviation limit theorems, in Prokhorov and Contemporary Probability Theory, eds
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Large deviation probabilities for sums of censored random variables with regularly varying distribution tails
For censored sums of regularly varying random variables, the paper derives uniform large-deviation asymptotics for all threshold values of order the cap, with explicit formulas near and between multiples of the cap.