Precise large deviations for sums of two-dimensional random vectors with dependent components of heavy tails

Abstract

ABSTRACTThis article focuses on the tail probabilities of the partial sums and the random sums , where is a sequence of independent identically distributed non-negative random vectors with two dependent components (using copulas for operational risk measurement) having extended regularly varying tails, and N(t) is a counting process independent of the sequence . Under some reasonable assumptions, some precise large deviation results for and are obtained in the componentwise way.