Local precise large deviations for sums of random variables with [formula omitted]-regularly varying densities

Abstract

In this paper we establish a local precise large deviation result for sums S n , n = 1 , 2 , … of independent and identically distributed random variables X 1 , X 2 , … with O -regularly varying densities f . The asymptotic behavior of the probability P ( x < S n − E S n ≤ x + T ) is comparable, for fixed T , with quantities n T f ( x + E X 1 ) or n ( F ( x + T ) − F ( x ) ) .