caa a22 4500 605463875 CHVBK 20210128100255.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s10687-015-0228-y doi (NATIONALLICENCE)springer-10.1007/s10687-015-0228-y Phantom distribution functions for some stationary sequences [Elektronische Daten] [Paul Doukhan, Adam Jakubowski, Gabriel Lang] The notion of a phantom distribution function (phdf) was introduced by O'Brien (Ann. Probab. 15, 281-292 (1987)). We show that the existence of a phdf is a quite common phenomenon for stationary weakly dependent sequences. It is proved that any α-mixing stationary sequence with continuous marginals admits a continuous phdf. Sufficient conditions are given for stationary sequences exhibiting weak dependence, what allows the use of attractive models beyond mixing. The case of discontinuous marginals is also discussed for α-mixing. Special attention is paid to examples of processes which admit a continuous phantom distribution function while their extremal index is zero. We show that Asmussen (Ann. Appl. Probab. 8, 354-374 1998) and Roberts et al. (Extremes. 9, 213-229 2006) provide natural examples of such processes. We also construct a non-ergodic stationary process of this type. The Author(s), 2015 Strictly stationary processes nationallicence Extremes nationallicence Extremal index nationallicence Phantom distribution function nationallicence α -mixing nationallicence Weak dependence nationallicence Lindley's process nationallicence Random walk Metropolis algorithm nationallicence Doukhan Paul Université de Cergy-Pontoise and Institut Universitaire de France, UMR 8088 Analyse, Géométrie et Modélisation, 2, av. Adolphe Chauvin, 95302, Cergy-Pontoise CEDEX, France aut Jakubowski Adam Nicolaus Copernicus University, Faculty of Mathematics and Computer Science, ul. Chopina 12/18, 87-100, Toruń, Poland aut Lang Gabriel AgroParisTech, UMR 518 Mathématique et Informatique appliquées, 19 avenue du Maine, 75732, Paris CEDEX 15, France aut Extremes Springer US; http://www.springer-ny.com 18/4(2015-12-01), 697-725 1386-1999 18:4<697 2015 18 10687 https://doi.org/10.1007/s10687-015-0228-y text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10687-015-0228-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Doukhan Paul Université de Cergy-Pontoise and Institut Universitaire de France, UMR 8088 Analyse, Géométrie et Modélisation, 2, av. Adolphe Chauvin, 95302, Cergy-Pontoise CEDEX, France aut NATIONALLICENCE 700 1- Jakubowski Adam Nicolaus Copernicus University, Faculty of Mathematics and Computer Science, ul. Chopina 12/18, 87-100, Toruń, Poland aut NATIONALLICENCE 700 1- Lang Gabriel AgroParisTech, UMR 518 Mathématique et Informatique appliquées, 19 avenue du Maine, 75732, Paris CEDEX 15, France aut NATIONALLICENCE 773 0- Extremes Springer US; http://www.springer-ny.com 18/4(2015-12-01), 697-725 1386-1999 18:4<697 2015 18 10687