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On reduction of two-parameter prediction problems. (English) Zbl 0822.60038

Summary: 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 \(S_ 2 \subseteq G_ 2\) to results for weakly stationary processes on \(G_ 1 \times G_ 2\) with observed values on \(G_ 1 \times S_ 2\). In particular, the method is applied to obtain new proofs of some well-known results of Tse-Pei Chiang [Dokl. Akad. Nauk SSSR 112, 207-210 (1957; Zbl 0082.343) and Teor. Veroyatn. Primen. 2, 60-91 (1957; Zbl 0082.343)].

MSC:

60G25 Prediction theory (aspects of stochastic processes)

Citations:

Zbl 0082.343
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