Hitting probabilities for Lévy processes on the real line
Abstract
We prove sharp two-sided estimates on the tail probability of the first hitting time of bounded interval as well as its asymptotic behaviour for general non-symmetric processes which satisfy an integral condition \[ \int_0^{\infty} \frac{d\xi}{1+\operatorname{Re} \psi(\xi)}<\infty. \] To this end, we first prove and then apply the global scale invariant Harnack inequality. Results are obtained under certain conditions on the characteristic exponent. We provide a wide class of Lévy processs which satisfy these assumptions.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2019
- DOI:
- 10.48550/arXiv.1911.05149
- arXiv:
- arXiv:1911.05149
- Bibcode:
- 2019arXiv191105149G
- Keywords:
-
- Mathematics - Probability;
- 60G51;
- 60J45;
- 60J50;
- 60J75