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arXiv · 0804.3169

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

Zbigniew Palmowski·Martijn Pistorius
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Abstract

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 Lévy process $X$ that admits exponential moments. The proof is based on a renewal argument and a two-dimensional renewal theorem of Höglund (1990).

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Zbigniew Palmowski, Martijn Pistorius. 2009-04-26. Cramér asymptotics for finite time first passage probabilities of general Lévy processes. https://arxiv.org/abs/0804.3169

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