Commutative nonstationary stochastic fields

Hatamleh Ra'ed

Address. Department of Mathematics, Irbid National University, P.O.Box 2600, Irbid, JORDAN


Abstract. The present paper is devoted to further development of commutative nonstationary field themes; the first studies in this area were performed by K.~Kirchev and V.~Zolotarev \cite{4, 5}. In this paper a more complicated variant of commutative field with nonstationary rank 2, carrying into more general situation for correlation function is studied. A condition of consistency (see (7) below) for commutative field is placed in the basis of the method proposed in \cite{4, 5} and developed in this paper. The following semigroup structures of correlation theory for disturbances and semigroups are used in this case: $T_t (\varepsilon)=\exp (it A_{\varepsilon})$, $A_\varepsilon = A_1 +\varepsilon A_2$, $|\varepsilon| \ll 1$.

AMSclassification. Primary 47D03; Secondary 47C10, 47F05.

Keywords. Commutative nonstationary stochastic fields, correlation function, infinitesimal correlation function, contractive semigroup.