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Mixing of linear spatial random fields. (Mélange pour des processus linéaires spatiaux.) (French) Zbl 0734.60054

Summary: We give sufficient strong mixing conditions for random fields \(X=(X_ t)_{t\in {\mathbb{Z}}^ d}\) defined linearly by \(X_ t=\sum_{s\in {\mathbb{Z}}^ d}g_{t,s}Z_ s\), where Z is itself a mixing random field, extending a work by V. V. Gorodetskij [Theory Probab. Appl. 22(1977), 411-413 (1978); translation from Teor. Veroyatn. Primen. 22, 421-423 (1977; Zbl 0377.60046)] concerned with unilateral linear sequences. We give explicit bounds for those mixing coefficients, they usually depend on the cardinal of the subsets considered, at least for \(d\geq 2\). We compare this case to the Gaussian one communicated by I. A. Ibragimov [Communication oracle, Orsay, 1991].

MSC:

60G60 Random fields

Citations:

Zbl 0377.60046
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