Cram\'{e}r asymptotics for finite time first passage probabilities of general L\'{e}vy processes
Probability
2009-04-26 v2
Abstract
We derive the exact asymptotics of if and tend to infinity with constant, for a L\'{e}vy process that admits exponential moments. The proof is based on a renewal argument and a two-dimensional renewal theorem of H\"{o}glund (1990).
Cite
@article{arxiv.0804.3169,
title = {Cram\'{e}r asymptotics for finite time first passage probabilities of general L\'{e}vy processes},
author = {Zbigniew Palmowski and Martijn Pistorius},
journal= {arXiv preprint arXiv:0804.3169},
year = {2009}
}