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2010 Exponential Moments of First Passage Times and Related Quantities for Random Walks
Alexander Iksanov, Matthias Meiners
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Electron. Commun. Probab. 15: 365-375 (2010). DOI: 10.1214/ECP.v15-1569

Abstract

For a zero-delayed random walk on the real line, let $\tau(x)$, $N(x)$ and $\rho(x)$ denote the first passage time into the interval $(x,\infty)$, the number of visits to the interval $(-\infty,x]$ and the last exit time from $(-\infty,x]$, 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 $x \to \infty$.

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Alexander Iksanov. Matthias Meiners. "Exponential Moments of First Passage Times and Related Quantities for Random Walks." Electron. Commun. Probab. 15 365 - 375, 2010. https://doi.org/10.1214/ECP.v15-1569

Information

Accepted: 26 September 2010; Published: 2010
First available in Project Euclid: 6 June 2016

zbMATH: 1235.60118
MathSciNet: MR2726084
Digital Object Identifier: 10.1214/ECP.v15-1569

Subjects:
Primary: 60K05
Secondary: 60G40

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