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Limit theorems for point random fields defined on the plane. (English. Russian original) Zbl 0731.60047

Ukr. Math. J. 43, No. 1, 98-100 (1991); translation from Ukr. Mat. Zh. 43, No. 1, 118-121 (1991).
Let \(\{N^ n\}\) be a sequence of two-parameter point random fields, field \(N^ n\) is adapted to filration \({\mathcal F}^ n\). The paper comprises sufficient conditions under which the sequence of fields \(\{N^ n\}\) converges weakly (i.e. in the Skorokhod topology) to the point field N with independent increments, whose finite-dimensional distributions are known. Conditions are formulated in terms of different types of compensators of fields \(\{N^ n\}\) with respect to filtrations \(\{\) \({\mathcal F}^ n\}\).

MSC:

60G60 Random fields
60B10 Convergence of probability measures
60F05 Central limit and other weak theorems
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References:

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