Exponential Moments of First Passage Times and Related Quantities for Random Walks
Alexander Iksanov, National T. Shevchenko University of Kiev
Matthias Meiners, Uppsala University
Abstract
For a zero-delayed random walk on the real line, let $τ(x)$,
$N(x)$ and $ρ(x)$ denote the first passage time into the
interval $(x,∞)$, the number of visits to the interval
$(-∞,x]$ and the last exit time from $(-∞,x]$,
respectively. In the present paper, we provide ultimate criteria
for the finiteness of exponential moments of these quantities.
Moreover, whenever these moments are finite, we derive their
asymptotic behaviour, as $x → ∞$.
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