Second order subexponential distributions with finite mean and their applications to subordinated distributions

Consider a probability distribution subordinate to a subexponential distribution with finite mean. In this paper, we discuss the second order tail behavior of the subordinated distribution within a rather general framework in which we do not require the existence of density functions. For this aim, the so-called second order subexponential distribution is proposed and some related properties of its are established. Our results unified and improved some classical results.