Potential Theory of Normal Tempered Stable Process

TL;DR

This paper investigates the potential theory of normal tempered stable processes, analyzing their potential and Levy densities, and compares these with the normal inverse Gaussian process, providing asymptotic behaviors and Green functions.

Contribution

It offers new insights into the potential theory of normal tempered stable processes and extends results to the normal inverse Gaussian process.

Findings

Asymptotic behavior of potential density and Levy density analyzed.

Green function and Levy density for the process characterized.

Results extend to the normal inverse Gaussian 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.