Tail behavior of the sums of dependent and heavy-tailed random variables

In this paper, we investigate the tail asymptotic behavior of the partial sums, the random sums and the weighted sums of heavy-tailed random variables (r.v.s.) under two new dependence structures, respectively. The increments are real-valued and have subexponential∗∗ distributions, and the dependence structures can contain common linearly negatively quadrant dependent r.v.s., some positively dependent r.v.s. and some other r.v.s. The obtained results are used to derive the asymptotic estimation of the finite-time ruin probability for a nonstandard renewal risk model. In addition, some mutual relations among these two new dependence structures and some other relevant ones are discussed.