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Moments of the number of upcrossings of an absolutely continuous process at points of density of a sample path derivative associated set

Author

Listed:
  • Anderson, Douglas R.
  • Carpenter, Daniel D.

Abstract

For a separable process on the unit interval with a.s. absolutely continuous sample paths a kth factorial moment formula is found for the number of sample path upcrossings of zero which occur at points of density (in a weak sense) of the set where the sample path derivative exceeds a fixed value. In the case where the sample path derivative is continuous on the closed unit interval the moment formula reduces to a simple variation of the Cramér-Leadbetter formula for the corresponding kth factorial moment of the number of unconstrained upcrossings.

Suggested Citation

  • Anderson, Douglas R. & Carpenter, Daniel D., 1982. "Moments of the number of upcrossings of an absolutely continuous process at points of density of a sample path derivative associated set," Stochastic Processes and their Applications, Elsevier, vol. 13(1), pages 27-37, July.
  • Handle: RePEc:eee:spapps:v:13:y:1982:i:1:p:27-37
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