LAUSR

Let {Xi = (X1,i,...,Xm,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 X1 are allowed to be generally dependent. Moreover, let N(·) be a nonnegative integer-valued process, independent of the sequence {Xi, i ≥ 1}. Under several mild assumptions, precise large deviations for Sn = Σi=1nXi and SN(t) = Σi=1N(t)Xi are investigated. Meanwhile, some simulation examples are also given to illustrate the results.