# Hunt's Hypothesis (H) for Markov Processes: Survey and Beyond

## TL;DR

This paper surveys Hunt's hypothesis (H) for Markov processes and Le9vy processes, explores multidimensional cases, and discusses open questions for future research.

## Contribution

It provides a comprehensive survey of Hunt's hypothesis (H), investigates multidimensional Le9vy processes, and highlights open problems in the field.

## Key findings

- Survey of existing results on Hunt's hypothesis (H)
- Analysis of (H) for multidimensional Le9vy processes
- Identification of open questions for future research

## Abstract

The goal of this paper is threefold. First, we survey the existing results on Hunt's hypothesis (H) for Markov processes and Getoor's conjecture for L\'{e}vy processes. Second, we investigate (H) for multidimensional L\'{e}vy processes from the viewpoints of projections and energy, respectively. Third, we present a few open questions for further study.