English

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 P(suputX(u)>x)P(\sup_{u\leq t}X(u) > x) if xx and tt tend to infinity with x/tx/t constant, for a L\'{e}vy process XX that admits exponential moments. The proof is based on a renewal argument and a two-dimensional renewal theorem of H\"{o}glund (1990).

Keywords

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}
}
R2 v1 2026-06-21T10:32:50.165Z