On the simulation of random fields. I (Q2740445)

This work is devoted to the construction of models of random fields which admit representation in the form of stochastic integrals. These models approximate fields with the given exactness and reliability in various functional spaces, namely, in \(L_{p},\) some Orlicz spaces and the space of continuous functions. As examples, models of homogeneous and homogeneous isotropic random fields in \(R^{d}\) are considered. All results are obtained for strictly sub-Gaussian random fields. The authors use their previous results [ibid. 58, 51-66 (1999); resp. ibid. 58, 45-60 (1998; Zbl 0942.60040) and ibid. 59, 77-92 (1999); resp. ibid. 59, 75-90 (1998; Zbl 0960.60049)] to obtain the assertions of this paper.