On weak convergence of random fields
Copyright policy )On weak convergence of random fields
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 \(D\).
weak convergence and tightness of probability measures, random fields, Central limit and other weak theorems, Random fields, compactness
weak convergence and tightness of probability measures, random fields, Central limit and other weak theorems, Random fields, compactness
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