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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Pages: 365-375

Publication Date: September 26, 2010

DOI: 10.1214/ECP.v15-1569

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