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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 (a1)
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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References
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Advances in Applied Probability
  • ISSN: 0001-8678
  • EISSN: 1475-6064
  • URL: /core/journals/advances-in-applied-probability
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