On the rate of convergence in the Poisson approximation for exceedances of high levels by stationary Gaussian processes. - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Applied Probability Année : 1997

On the rate of convergence in the Poisson approximation for exceedances of high levels by stationary Gaussian processes.

Marie Kratz
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Holger Rootzén
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Résumé

Let ${\xi(t); t\geq 0}$ be a normalized continuous mean square differentiable stationary normal process with covariance function r(t). Further, let $$ \rho(t)=\frac{(1-r(t))^2}{1-r(t)^2+r'(t)|r'(t)|} $$ and set $$ \delta=\frac{1}{2}\wedge \inf_{t\geq 0} \rho(t). $$ We give bounds which are roughly of the order $T^{-\delta}$ for the rate of convergence of the distribution of the maximum and of the number of upcrossings of a high level by $\xi(t)$ in the interval [0,T]. The results assume that r(t) and r'(t) decay polynomially at infinity and that r''(t) is suitably bounded. For the number of upcrossings it is in addition assumed that r(t) is non-negative.
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Dates et versions

hal-00179383 , version 1 (15-10-2007)

Identifiants

  • HAL Id : hal-00179383 , version 1

Citer

Marie Kratz, Holger Rootzén. On the rate of convergence in the Poisson approximation for exceedances of high levels by stationary Gaussian processes.. Journal of Applied Probability, 1997, 34 (4), pp.908-923. ⟨hal-00179383⟩
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