\(C\)-tightness criterion for non-adapted random fields (Q2368164)

The paper contains sufficient conditions of \(C\)-tightness of nonadapted two-parameter random fields. The sequence \((X^ n)\) of random fields is called \(C\)-tight if the sequence of distributions or laws \(L(X^ n)\) is tight on \((D,B(D))\) and every limit point is concentrated on \(C\). The conditions of \(C\)-tightness are formulated in terms of increments \(\sup_{0\leq v\leq N} | x^ n(k_ i(\sigma,v))-x^ n(k_ i(\tau,v))|\), \(|\sigma-\tau|<\delta\), \(k_ 1(u,v)=(u,v)\), \(k_ 2(u,v)=(v,u)\), and are similar to those ones for adapted fields.