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Moments for First-Passage and Last-Exit Times, the Minimum, and Related Quantities for Random Walks with Positive Drift

Svante Janson
Advances in Applied Probability
Vol. 18, No. 4 (Dec., 1986), pp. 865-879
DOI: 10.2307/1427253
Stable URL: http://www.jstor.org/stable/1427253
Page Count: 15
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Moments for First-Passage and Last-Exit Times, the Minimum, and Related Quantities for Random Walks with Positive Drift
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Abstract

Consider the sequence of partial sums of a sequence of i.i.d. random variables with positive expectation. We study various random quantities defined by the sequence of partial sums, e.g. the time at which the first or last crossing of a given level occurs, the value of the partial sum immediately before or after the crossing, the minimum of all partial sums. Necessary and sufficient conditions are given for the existence of moments of these quantities.

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