On the simulation of random fields. I. (English. Ukrainian original) Zbl 0985.60036

Kozachenko, Yu. V.; Pashko, A. O.

Theory Probab. Math. Stat. 61, 61-74 (2000); translation from Teor. Jmovirn. Mat. Stat. 61, 59-71 (2000).

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.

Reviewer: A.V.Swishchuk (Kyïv)

MSC:

60G17	Sample path properties
60G60	Random fields
60H05	Stochastic integrals
60G07	General theory of stochastic processes

Keywords:

strictly sub-Gaussian random fields; stochastic integrals; Orlicz space; modelling of random fields

Citations:

Zbl 0942.60040; Zbl 0960.60049