Large deviations for random sums of negatively dependent random variables with consistently varying tails

Abstract

Let { X k , k = 1 , 2 , … } be a sequence of negatively dependent random variables with common distribution F and finite expectation μ . Under the assumption that the tail probability F ¯ ( x ) = 1 - F ( x ) is consistently varying as x tends to infinity, this paper investigates precise large deviations for the random sum S N ( t ) = ∑ n = 1 N ( t ) X n , where { N ( t ) , t ⩾ 0 } is a nonnegative and integer-valued process independent of { X k , k = 1 , 2 , … } .