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.
Regular Variation (Cambridge Uni- versity Press, Cambridge, 1987)
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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.