Distribution of some functionals for a L\'evy process with matrix-exponential jumps of the same sign

TL;DR

This paper develops a matrix-based framework for analyzing fluctuation theory in Lévy processes with matrix-exponential jumps, generalizing known results for specific jump distributions.

Contribution

It introduces a matrix form of the infinitely divisible factorization components for Lévy processes with matrix-exponential jumps, extending existing results.

Findings

Matrix form of the infinitely divisible factorization components

Generalizations of fluctuation results for specific jump distributions

Framework applicable to Lévy processes with matrix-exponential jumps

Abstract

This paper provides a framework for investigations in fluctuation theory for L\'evy processes with matrix-exponential jumps. We present a matrix form of the components of the infinitely divisible factorization. Using this representation we establish generalizations of some results known for compound Poisson processes with exponential jumps in one direction and generally distributed jumps in the other direction.