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1 results

  • Simple random walk statistics. Part I: Discrete time results

  • Part of
  • W. Katzenbeisser, W. Panny
  • Journal:
    Journal of Applied Probability / Volume 33 / Issue 2 / September 1996
    Published online by Cambridge University Press:
    14 July 2016, pp. 311-330
    Print publication:
    September 1996

  • In a famous paper, Dwass (1967) proposed a method to deal with rank order statistics, which constitutes a unifying framework to derive various distributional results. In the present paper an alternative method is presented, which allows us to extend Dwass's results in several ways, namely arbitrary endpoints, horizontal steps and arbitrary probabilities for the three step types. Regarding these extensions the pertaining rank order statistics are extended as well to simple random walk statistics. This method has proved appropriate to generalize all results given by Dwass. Moreover, these discrete time results can be taken as a starting point to derive the corresponding results for randomized random walks by means of a limiting process.