A NOTE ON R-BALAYAGES OF MATRIX-EXPONENTIAL LEVY PROCESSES

Abstract

In this note we give semi-explicit solutions for r-balayages of matrix-exponential Levy processes. To this end, we turn to an identity for the joint Laplace transform of the first entry time and the undershoot and a semi-explicit solution of the negative Wiener-Hopf factor. Our result is closely related to the works by Mordecki in [11], Asmussen, Avram and Pistorius in [3], Chen, Lee and Sheu in [7], and many others.