On the rate of convergence for extremes of mean square differentiable stationary normal processes

Journal of Applied Probability

Volumn 34, Issue 4, 1997, Pages 908-923

  Kratz, Marie F ^a   Rootzén, Holger ^b  

^a UNIVERSITÉ PARIS DESCARTES   (France)

^b CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

Extremes; Normal processes; Poisson convergence; Rate of convergence

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIATION (CALCULUS); FUNCTIONS; POISSON DISTRIBUTION; POLYNOMIALS; SPECTRUM ANALYSIS;

COVARIANCE FUNCTION; NORMAL PROCESSES; POISSON CONVERGENCE;

RANDOM PROCESSES;

EID: 0031295111     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0021900200101615     Document Type: Article

References (13)

1. HARBOUR, A. D., HOLST, L. AND JANSON, S. (1992) Poisson Approximation. Oxford Science Publishers, Oxford.
2. BERMAN, S. M. (1971) Excursions above high levels for stationary Gaussian processes. Pacific J. Math. 36, 63-79.
3. CRAMÉR, H. (1965) A limit theorem for the maximum values of certain stochastic processes. Theory Prob. Appl. 10, 126-128.
4. CRAMÉR, H. AND LEADBETTER, M. R. (1967) Stationary and Related Stochastic Processes. Wiley, New York.
5. FALK, M., HÜSLER, J. AND REISS, R. D. (1994) Laws of Small Numbers: Extremes and Rare Events. Birkhaüser, Basel.
6. HOLST, L. AND JANSON, S. (1990) Poisson approximation using the Stein-Chen method and coupling: number of exceedances of Gaussian random variables. Ann. Prob. 18, 713-723.
7. LEADBETTER, M. R., LINDGREN, G. AND ROOTZÉN, H. (1978) Conditions for the convergence in distribution of maxima of stationary normal processes. Stoch. Proc. Appl 8. 131-139.
8. LEADBETTER, M. R., LINDGREN, G. AND ROOTZÉN, H. (1983) Extremes and Related Properties of Random Sequences and Processes. Springer, New York.
9. PICKERSGILL, E. A. AND PITERBARG, V. I. (1987) Estimation of the rate of convergence in a Poisson limit theorem for the excursions of stationary Gaussian processes. Theory Prob. Math. Statist. 36 (in Russian).
10. PICKANDS, J., III (1969) Upcrossing probabilities for stationary Gaussian processes. Trans. Amer. Math. Soc. 145, 51-73.
11. PITERBARG, V. I. (1982) Large deviations of random processes close to Gaussian ones. Theory Prob. Appl. 27, 504-524.
12. ROOTZÉN, H. (1983) The rate of convergence of extremes of stationary normal sequences. Adv. Appl. Prob. 15, 54-80.
13. VOLKONSKII, V. A. AND ROZANOV, Yu. A. (1961) Some limit theorems for random functions II. Theory Prob. Appl. 6, 186-198.