Space-time boundedness and asymptotic behaviors of the densities of CM E-subordinators

In this article, we consider subordinators whose L & eacute;vy measures are represented as Laplace transforms of measures on (0,infinity). We shall call them CME-subordinators. Transition probabilities of such processes without drifts are absolutely continuous on (0,infinity) with respect to Lebesgue measure on (0,infinity). We show that the densities are space-time bounded on [t(1),infinity)x[x(1),infinity) for each t(1)>0 and x(1)>0, and the supremum of the densities with respect to space variable tends to zero as time goes to infinity. Moreover, we point out that the speed of decrease is closely related to the behavior near the origin of the corresponding L & eacute;vy density.

Automated summary

This article considers subordinators whose Lévy measures are represented as Laplace transforms of measures on (0,infinity), and refers to them as CME-subordinators. The study shows that the transition probabilities of such processes without drifts are absolutely continuous on (0,infinity) with respect to Lebesgue measure. It is also demonstrated that the densities are bounded in space-time and tend to zero as time goes to infinity, with the speed of decrease being closely related to the behavior near the origin of the corresponding Lévy density.