Estimates on transition densities of subordinators with jumping density decaying in mixed polynomial orders

Abstract: In this paper, we discuss estimates on transition densities for subordinators, which are global in time. We establish the sharp two-sided estimates on the transition densities for subordinators whose L\'evy measures are absolutely continuous and decaying in mixed polynomial orders. Under a weaker assumption on L\'evy measures, we also obtain a precise asymptotic behaviors of the transition densities at infinity. Our results cover geometric stable subordinators, Gamma subordinators and much more.