Rate of Poisson approximation of the number of exceedances of nonstationary normal sequences. - Archive ouverte HAL
Article Dans Une Revue Stochastic Processes and their Applications Année : 1995

Rate of Poisson approximation of the number of exceedances of nonstationary normal sequences.

Marie Kratz
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  • PersonId : 1163150
Jürg Hüsler
  • Fonction : Auteur
  • PersonId : 843424

Résumé

It is known that the partial maximum of nonstationary Gaussian sequences converges in distribution and that the number of exceedances of a boundary is asymptotically a Poisson random variable, under certain restrictions. We investigate the rate of Poisson approximation for the number of exceedances. We generalize the result known in the stationary case, showing that the given bound of the rate depends on the largest positive auto-correlation value (less than 1) and the lowest values of the nonconstant boundary. We show that for special cases this bound cannot be improved.

Dates et versions

hal-00179421 , version 1 (15-10-2007)

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Citer

Marie Kratz, Jürg Hüsler. Rate of Poisson approximation of the number of exceedances of nonstationary normal sequences.. Stochastic Processes and their Applications, 1995, 55 (2), pp.301-313. ⟨10.1016/0304-4149(94)00036-S⟩. ⟨hal-00179421⟩
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