Let L and S denote the classes of distributions with long tails and subexponential tails respectively. Let OS denote the class of distributions with O-subexponential tails, which means the distributions with the tails having the same order as the tails of their 2-fold convolutions. In this...

In this paper, we establish the second order asymptotics of ruin probabilities of a renewal risk model under the condition that the equilibrium distribution of claim sizes belongs to a rather general heavy-tailed distribution subclass—the class of second order subexponential distributions with...

We establish a one-sided large deviation local limit theorem for sums of i.i.d. rv's with heavy tails assuming only a condition on the one-sided tail of the generic distribution. The results in [Baltrunas, A., 1996. A local limit theorem on one-sided large deviations for dominated-variation...

Let {Xn;n[greater-or-equal, slanted]1} be an arbitrary sequence of heavy-tailed random variables, independent of a process of nonnegative, integer-valued rv's {N(t);t[greater-or-equal, slanted]0}. In this paper, we present a necessary and a sufficient condition on {N(t);t[greater-or-equal,...