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Moments for First-Passage and Last-Exit Times, the Minimum, and Related Quantities for Random Walks with Positive Drift
Advances in Applied Probability
Vol. 18, No. 4 (Dec., 1986), pp. 865-879
Published by: Applied Probability Trust
Stable URL: http://www.jstor.org/stable/1427253
Page Count: 15
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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.
Advances in Applied Probability © 1986 Applied Probability Trust