On the Lengths of Excursions of Some Markov Processes

  title={On the Lengths of Excursions of Some Markov Processes},
  author={Jim Pitman and Marc Yor},
Results are obtained regarding the distribution of the ranked lengths of component intervals in the complement of the random set of times when a recurrent Markov process returns to its starting point. Various martingales are described in terms of the L evy measure of the Poisson point process of interval lengths on the local time scale. The martingales derived from the zero set of a one-dimensional di usion are related to martingales studied by Az ema and Rainer. Formulae are obtained which… CONTINUE READING
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