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Bounds for the expected number of level crossings of certain harmonizable infinitely divisible processes

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  • Marcus, Michael B.
  • Shen, Kevin

Abstract

Let denote the expected number of crossings of a level , in a fixed time interval [0,1], by a large class of real valued symmetric stationary harmonizable infinitely divisible processes which includes stationary harmonizable stable processes. Equivalent upper and lower bounds are given for and a precise asymptotic limit is given for , as .

Suggested Citation

  • Marcus, Michael B. & Shen, Kevin, 1998. "Bounds for the expected number of level crossings of certain harmonizable infinitely divisible processes," Stochastic Processes and their Applications, Elsevier, vol. 76(1), pages 1-32, August.
    • Handle: RePEc:eee:spapps:v:76:y:1998:i:1:p:1-32
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    References listed on IDEAS

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    1. Marcus, Michael B., 1989. "Some bounds for the expected number of level crossings of symmetric harmonizable p-stable processes," Stochastic Processes and their Applications, Elsevier, vol. 33(2), pages 217-231, December.
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