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2 results

  • On overshoots and hitting times for random walks

  • Jean Bertoin
  • Journal:
    Journal of Applied Probability / Volume 36 / Issue 2 / June 1999
    Published online by Cambridge University Press:
    14 July 2016, pp. 593-600
    Print publication:
    June 1999

  • Consider an oscillating integer valued random walk up to the first hitting time of some fixed integer x > 0. Suppose there is a fee to be paid each time the random walk crosses the level x, and that the amount corresponds to the overshoot. We determine the distribution of the sum of these fees in terms of the renewal functions of the ascending and descending ladder heights. The proof is based on the observation that some path transformation of the random walk enables us to translate the problem in terms of the intersection of certain regenerative sets.

  • Regenerative sets and subordinators

  • Cristina Gzyl
  • Journal:
    Journal of Applied Probability / Volume 14 / Issue 1 / March 1977
    Published online by Cambridge University Press:
    14 July 2016, pp. 217-220
    Print publication:
    March 1977

  • It has been shown that the probabilistic structure of a regular regenerative set can be described in terms of the exponent of an appropriate subordinator. We give a relation which expresses the distribution of two Markov processes associated with a regenerative set in terms of this exponent.