# 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

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topFriedrich, 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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- [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). Zbl0082.34302
- [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] 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. Zbl0622.60051
- [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. Zbl0332.60026
- [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] Yu. A. Rozanov, Stationary Stochastic Processes, Fizmatgiz, Moscow, 1963 (in Russian).

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