J-regularity of multivariate stationary sequences for some families J

• Autorzy: Klotz L. , Mädler C.
• Języki publikacji: EN

Abstrakty

EN

Let n ϵ N, S be a nonempty finite subset of the set of integers, S^c be its complement, and J be the family of translations of S^c by ln, l ϵ Z. For such a family, J-regularity of a q-variate stationary sequence over Z is studied. If S contains exactly n elements, a description of a J-regular sequence in terms of its spectral density is obtained. Some examples are given for the case where S contains more than n elements.

Słowa kluczowe

EN

multivariate stationary sequence; spectra density; J-regularity

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2015
• Tom: Vol. 35, Fasc. 1
• Strony: 31--40
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Klotz L.

• Universität Leipzig, Mathematisches Institut, PF 10 09 20, D-04009 Leipzig

autor

Mädler C.

• Universität Leipzig, Mathematisches Institut, PF 10 09 20, D-04009 Leipzig

Bibliografia

• [1] L. A. Bruckner, Interpolation of homogeneous random fields on discrete groups, Ann. Math. Statist. 40 (1969), pp. 251-258.
• [2] E. G. Gladyšev, Periodically correlated random sequences (in Russian), Dokl. Akad. Nauk SSSR 137 (1961), pp. 1026-1029.
• [3] A. Makagon, Theoretical prediction of periodically correlated sequences, Probab. Math. Statist. 19 (2) (1999), pp. 287-322.
• [4] A. Makagon, Stationary sequences associated with a periodically correlated sequence, Probab. Math. Statist. 31 (2) (2011), pp. 263-283.
• [5] A. Makagon and A. Miamee, Spectral representation of periodically correlated sequences, Probab. Math. Statist. 33 (1) (2013), pp. 175-188.
• [6] A. Makagon and A. Weron, Wold-Cramér concordance theorems for interpolation of q-variate stationary processes over locally compact Abelian groups, J. Multivariate Anal. 6 (1976), pp. 123-137.
• [7] H. Salehi and J. K. Scheidt, Interpolation of q-variate weakly stationary stochastic processes over a locally compact abelian group, J. Multivariate Anal. 2 (1972), pp. 307-331.
• [8] A. Weron, On characterizations of interpolable and minimal stationary processes, Studia Math. 49 (1973/74), pp. 165-183.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).