On weak convergence of random fields (Q5915352)
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scientific article; zbMATH DE number 1466095
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On weak convergence of random fields |
scientific article; zbMATH DE number 1466095 |
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On weak convergence of random fields (English)
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16 February 2001
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A criterion of compactness is established for sets in the space \(D\) introduced by the authors [ibid. 30, No. 3, 195-208 (1990), resp. ibid. 30, No. 3, 453-469 (1990; Zbl 0722.60012)]. This \(D\) consisting of functions on \([0,1]^2\) whose discontinuity points lie on smooth curves is viewed with metric making it a Polish space. Then conditions of tightness of probability measures on \((D,{\mathcal B}(D))\) are obtained and conditions of weak convergence of fields with trajectories in \(D\) follow. Markov fields with polygonal realizations [see \textit{T. Arak} and \textit{D. Surgailis}, Probab. Theory Relat. Fields 80, No. 4, 543-579 (1989; Zbl 0638.60091)] have trajectories in \(D\).
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weak convergence and tightness of probability measures
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compactness
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random fields
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