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A Note on the Dependence Conditions for Stationary Normal Sequences
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 Title & Authors
A Note on the Dependence Conditions for Stationary Normal Sequences
Choi, Hyemi;
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Extreme value theory concerns the distributional properties of the maximum of a random sample; subsequently, it has been significantly extended to stationary random sequences satisfying weak dependence restrictions. We focus on distributional mixing condition and the Berman condition based on covariance among weak dependence restrictions. The former is assumed for general stationary sequences and the latter for stationary normal processes; however, both imply the same distributional limit of the maximum of the normal process. In this paper condition is shown weaker than Berman's covariance condition. Examples are given where the Berman condition is satisfied but the distributional mixing is not.
Berman condition;covariance;extreme value theory;mixing condition;stationary normal sequence;
 Cited by
Berman, S. M. (1964). Limit theorems for the maximum term in stationary sequences, The Annals of Mathematical Statistics, 35, 319-329. crossref(new window)

Embrecht, P., Kluppelberg, C. and Mikosch, T. (1999). Modelling Extremal Events for Insurance and Finance, Springer, New York.

Leadbetter, M. R., Lindgren, G. and Rootzen, H. (1983). Extremes and Related Properties of Random Sequences and Processes, Springer, New York.

Leadbetter, M. R. and Rootzen, H. (1998). On extreme value theory in stationary random fields, In Stochastic Processes and Related Topics, in Memory of Stamatis Cambanis, Eds. Karatzas et al., 275-285 Springer, Boston.

Leadbetter, M. R., Rootzen, H. and Choi, H. (2000). On central limit theory for random additive functions under weak dependence restrictions, In State of the Art in Probability and Statistics, de Gunst et al., eds. IMS Lecture Note-Monograph Series #36, 464-476.

Lindgren, G. and Rootzen, H. (1987). Extreme values: theory and technical applications, Scandinavian Journal of Statistics, 14, 241-279.

Lukcas, E. (1970). Characteristic Functions, Hafner, New York.

Mittal, Y. (1979). A mixing condition for stationary Gaussian processes, The Annals of Probability, 7, 724-732. crossref(new window)

Turkman, K. F. (2006). A note on the extremal index for space-time processes, Journal of Applied Probability, 43, 114-126. crossref(new window)

Turner, R. and Chareka, P. (2012). A note on the Berman condition, The Brazilian Journal of Probability and Statistics, 25, 82-87.

Wintner, A. (2013). The Fourier Transforms of Probability Distributions, Literary Licensing, LLC.