Precise large deviations for sums of random vectors with dependent components of consistently varying tails

Abstract

Let {X i = (X 1,i ,...,X m,i )⊤, i ≥ 1} be a sequence of independent and identically distributed nonnegative m-dimensional random vectors. The univariate marginal distributions of these vectors have consistently varying tails and finite means. Here, the components of X 1 are allowed to be generally dependent. Moreover, let N(·) be a nonnegative integer-valued process, independent of the sequence {X i , i ≥ 1}. Under several mild assumptions, precise large deviations for S n = Σ i=1 n X i and S N(t) = Σ i=1 N(t) X i are investigated. Meanwhile, some simulation examples are also given to illustrate the results.