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- W3088508716 abstract "For a Lévy process $X$ on a finite time interval consider the probability that it exceeds some fixed threshold $x>0$ while staying below $x$ at the points of a regular grid. We establish exact asymptotic behavior of this probability as the number of grid points tends to infinity. We assume that $X$ has a zooming-in limit, which necessarily is $1/alpha $-self-similar Lévy process with $alpha in (0,2]$, and restrict to $alpha >1$. Moreover, the moments of the difference of the supremum and the maximum over the grid points are analyzed and their asymptotic behavior is derived. It is also shown that the zooming-in assumption implies certain regularity properties of the ladder process, and the decay rate of the left tail of the supremum distribution is determined." @default.
- W3088508716 created "2020-10-01" @default.
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- W3088508716 date "2020-01-01" @default.
- W3088508716 modified "2023-10-06" @default.
- W3088508716 title "Zooming-in on a Lévy process: failure to observe threshold exceedance over a dense grid" @default.
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- W3088508716 doi "https://doi.org/10.1214/20-ejp513" @default.
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