Electronic Communications in Probability

Exponential Moments of First Passage Times and Related Quantities for Random Walks

Alexander Iksanov and Matthias Meiners

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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 $x \to \infty$.

Article information

Electron. Commun. Probab., Volume 15 (2010), paper no. 34, 365-375.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K05: Renewal theory
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]

first-passage time last exit time number of visits random walk renewal theory

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Iksanov, Alexander; Meiners, Matthias. Exponential Moments of First Passage Times and Related Quantities for Random Walks. Electron. Commun. Probab. 15 (2010), paper no. 34, 365--375. doi:10.1214/ECP.v15-1569. https://projecteuclid.org/euclid.ecp/1465243977

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