On reduction of two-parameter prediction problems

J. Friedrich; L. Klotz; M. Riedel

Studia Mathematica (1995)

  • Volume: 114, Issue: 2, page 147-158
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Friedrich, J., Klotz, L., and Riedel, M.. "On reduction of two-parameter prediction problems." Studia Mathematica 114.2 (1995): 147-158. <http://eudml.org/doc/216185>.

@article{Friedrich1995,
abstract = {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.},
author = {Friedrich, J., Klotz, L., Riedel, M.},
journal = {Studia Mathematica},
keywords = {prediction; weakly stationary processes; locally compact Abelian group},
language = {eng},
number = {2},
pages = {147-158},
title = {On reduction of two-parameter prediction problems},
url = {http://eudml.org/doc/216185},
volume = {114},
year = {1995},
}

TY - JOUR
AU - Friedrich, J.
AU - Klotz, L.
AU - Riedel, M.
TI - On reduction of two-parameter prediction problems
JO - Studia Mathematica
PY - 1995
VL - 114
IS - 2
SP - 147
EP - 158
AB - 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.
LA - eng
KW - prediction; weakly stationary processes; locally compact Abelian group
UR - http://eudml.org/doc/216185
ER -

References

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  1. [1] R. Cheng, A strong mixing condition for second-order stationary random fields, Studia Math. 101 (1992), 139-153. Zbl0809.60061
  2. [2] J. Dixmier, Von Neumann Algebras, North-Holland, Amsterdam, 1981. 
  3. [3] P. Hennequin and A. Tortrat, Probability Theory and its Applications, Nauka, Moscow, 1974 (in Russian). 
  4. [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). Zbl0082.34302
  5. [5] Z. P. Jiang, On linear extrapolation of a discrete homogeneous random field, Dokl. Akad. Nauk SSSR 112 (1957), 207-210 (in Russian). Zbl0082.34301
  6. [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. [7] A. Makagon and H. Salehi, Stationary fields with positive angle, J. Multivariate Anal. 22 (1987), 106-125. Zbl0622.60051
  8. [8] A. Makagon and A. Weron, q-variate minimal stationary processes, Studia Math. 59 (1976), 41-52. 
  9. [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. Zbl0332.60026
  10. [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. Zbl0129.08902
  11. [11] Yu. A. Rozanov, Stationary Stochastic Processes, Fizmatgiz, Moscow, 1963 (in Russian). 

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