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On multiple-level excursions by stationary processes with deterministic peaks

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  • Hsing, Tailen
  • Leadbetter, M. R.

Abstract

A well-known property of stationary Gaussian processes is that the excursions over high levels ("peaks") have a limiting parabolic shape, each determined by a single random parameter. This means, in particular, that (in the limit) the length of a single excursion above a high level determines the length of the (shorter) excursion above each higher level. In this paper we consider a general class of stationary processes with this property. Results of Leadbetter and Hsing (1990) for convergence of exceedance random measures are generalized to include multiple-level exceedances and developed further for the above class of processes. Specific application is made to stationary normal processes.

Suggested Citation

  • Hsing, Tailen & Leadbetter, M. R., 1997. "On multiple-level excursions by stationary processes with deterministic peaks," Stochastic Processes and their Applications, Elsevier, vol. 71(1), pages 11-32, October.
    • Handle: RePEc:eee:spapps:v:71:y:1997:i:1:p:11-32
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    1. Leadbetter, M. R. & Hsing, Tailen, 1990. "Limit theorems for strongly mixing stationary random measures," Stochastic Processes and their Applications, Elsevier, vol. 36(2), pages 231-243, December.
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