Geodesic
Commutative nonstationary stochastic fields
Archivum mathematicum, Tome 38 (2002) no. 3, pp. 161-169
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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 [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 [4, 5] and developed in this paper. The following semigroup structures of correlation theory for disturbances and semigroups are used in this case: $T_t (\varepsilon )=\exp (it A_{\varepsilon })$, $A_\varepsilon = A_1 +\varepsilon A_2$, $|\varepsilon | \ll 1$.
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 [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 [4, 5] and developed in this paper. The following semigroup structures of correlation theory for disturbances and semigroups are used in this case: $T_t (\varepsilon )=\exp (it A_{\varepsilon })$, $A_\varepsilon = A_1 +\varepsilon A_2$, $|\varepsilon | \ll 1$.
Classification : 47D99, 47N30, 60G12
Keywords: commutative nonstationary stochastic fields; correlation function; infinitesimal correlation function; contractive semigroup 
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Ra'ed, Hatamleh. Commutative nonstationary stochastic fields. Archivum mathematicum, Tome 38 (2002) no. 3, pp. 161-169. http://geodesic.mathdoc.fr/item/ARM_2002_38_3_a0/

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