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Poisson approximation of the number of exceedances of a discrete-time x2-process

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  • Raab, Mikael

Abstract

Consider a discrete-time x2-process, i.e. a process defined as the sum of squares of independent and identically distributed Gaussian processes. Count the number of values that exceed a certain level. Let this level and the number of time points considered increase simultaneously so that the expected number of points above the level remains fixed. It is shown that the number of exceeding points converges to a Poisson distribution if the dependence in the underlying Gaussian processes is not too strong. By using the coupling approach of the Stein-Chen method, both limit theorems and rates of convergence are obtained.

Suggested Citation

  • Raab, Mikael, 1997. "Poisson approximation of the number of exceedances of a discrete-time x2-process," Stochastic Processes and their Applications, Elsevier, vol. 66(1), pages 41-54, February.
    • Handle: RePEc:eee:spapps:v:66:y:1997:i:1:p:41-54
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    References listed on IDEAS

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    1. Albin, J. M. P., 1992. "On the general law of iterated logarithm with application to selfsimilar processes and to Gaussian processes in n and Hilbert space," Stochastic Processes and their Applications, Elsevier, vol. 41(1), pages 1-31, May.
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