Hunt’s Hypothesis (H) for the Sum of Two Independent Lévy Processes
- Resource Type
- Authors
- Ze-Chun Hu; Wei Sun
- Source
- Communications in Mathematics and Statistics. 6:227-247
- Subject
- Statistics and Probability
Large class
Primary: 60J45, Secondary: 60G51
Mathematics::Complex Variables
Applied Mathematics
Open problem
Probability (math.PR)
010102 general mathematics
Probabilistic logic
16. Peace & justice
01 natural sciences
Measure (mathematics)
Lévy process
Potential theory
010104 statistics & probability
Computational Mathematics
Mathematics::Probability
FOS: Mathematics
Point (geometry)
0101 mathematics
Mathematical economics
Mathematics - Probability
Mathematics
- Language
- ISSN
- 2194-671X
2194-6701
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.