Potential Theory of Normal Tempered Stable Process

Abstract

In this article, we study the potential theory of normal tempered stable process which is obtained by time-changing the Brownian motion with a tempered stable subordinator. Precisely, we study the asymptotic behavior of potential density and Levy density associated with tempered stable subordinator and the Green function and the Levy density associated with the normal tempered stable process. We also provide the corresponding results for normal inverse Gaussian process which is a well studied process in literature.