Cramér asymptotics for finite time first passage probabilities of general Lévy processes

Details Cramér asymptotics for finite time first passage probabilities of general Lévy processes Cramér asymptotics for finite time first passage probabilities of general Lévy processes

2008-04-19

arxiv.org/abs/0804.3169v2

Mathematics

Probability

Scientific paper

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

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