# Hunt's Hypothesis (H) for the Sum of Two Independent Levy Processes

## TL;DR

This paper investigates Hunt's hypothesis (H) for the sum of two independent Levy processes, providing new theorems, examples, and a novel Levy measure condition that ensures (H) for many one-dimensional Levy processes.

## Contribution

It introduces new theorems and a novel Levy measure condition that establish when Hunt's hypothesis (H) holds for sums of independent Levy processes.

## Key findings

- Theorems on (H) for sums of Levy processes
- Examples illustrating (H) validity
- A new Levy measure condition ensuring (H)

## Abstract

Which Levy processes satisfy Hunt's hypothesis (H) is a long-standing open problem in probabilistic potential theory. The study of this problem for one-dimensional Levy processes suggests us to consider (H) from the point of view of the sum of Levy processes. In this paper, we present theorems and examples on the validity of (H) for the sum of two independent Levy processes. We also give a novel condition on the Levy measure which implies (H) for a large class of one-dimensional Levy processes.