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1995 | 114 | 2 | 147-158
Tytuł artykułu

On reduction of two-parameter prediction problems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We present a general method for the extension of results about linear prediction for q-variate weakly stationary processes on a separable locally compact abelian group $G_2$ (whose dual is a Polish space) with known values of the processes on a separable subset $S_2 ⊆ G_2$ to results for weakly stationary processes on $G_1 × G_2$ with observed values on $G_1 × S_2$. In particular, the method is applied to obtain new proofs of some well-known results of Ze Pei Jiang.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
114
Numer
2
Strony
147-158
Opis fizyczny
Daty
wydano
1995
otrzymano
1994-04-11
poprawiono
1994-11-16
Twórcy
autor
  • Fachbereich Mathematik/Informatik, Universität Leipzig 04109, Leipzig, Germany
autor
  • Fachbereich Mathematik/Informatik, Universität Leipzig 04109, Leipzig, Germany
autor
  • Fachbereich Mathematik/Informatik, Universität Leipzig 04109, Leipzig, Germany
Bibliografia
  • [1] R. Cheng, A strong mixing condition for second-order stationary random fields, Studia Math. 101 (1992), 139-153.
  • [2] J. Dixmier, Von Neumann Algebras, North-Holland, Amsterdam, 1981.
  • [3] P. Hennequin and A. Tortrat, Probability Theory and its Applications, Nauka, Moscow, 1974 (in Russian).
  • [4] Z. P. Jiang, Extrapolation theory of a homogeneous random field with continuous parameters, Teor. Veroyatnost. i Primenen. 2 (1) (1957), 60-91 (in Russian).
  • [5] Z. P. Jiang, On linear extrapolation of a discrete homogeneous random field, Dokl. Akad. Nauk SSSR 112 (1957), 207-210 (in Russian).
  • [6] H. Korezlioglu and Ph. Loubaton, Prediction and spectral decomposition of wide sense stationary processes on $Z^2$, in: F. Droesbeke (ed.), Spatial Processes and Spatial Time Series Analysis, Proceedings of the 6th Franco-Belgian Meeting of Statisticians, November 1985, Bruxelles, 1985, 127-164.
  • [7] A. Makagon and H. Salehi, Stationary fields with positive angle, J. Multivariate Anal. 22 (1987), 106-125.
  • [8] A. Makagon and A. Weron, q-variate minimal stationary processes, Studia Math. 59 (1976), 41-52.
  • [9] 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), 123-137.
  • [10] M. Rosenberg, The square-integrability of matrix-valued functions with respect to a non-negative Hermitian measure, Duke Math. J. 31 (1964), 291-298.
  • [11] Yu. A. Rozanov, Stationary Stochastic Processes, Fizmatgiz, Moscow, 1963 (in Russian).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv114i2p147bwm
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