# Commutative nonstationary stochastic fields

Archivum Mathematicum (2002)

- Volume: 038, Issue: 3, page 161-169
- ISSN: 0044-8753

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topRa'ed, Hatamleh. "Commutative nonstationary stochastic fields." Archivum Mathematicum 038.3 (2002): 161-169. <http://eudml.org/doc/248951>.

@article{Raed2002,

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 [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: $T_t (\varepsilon )=\exp (it A_\{\varepsilon \})$, $A_\varepsilon = A_1 +\varepsilon A_2$, $|\varepsilon | \ll 1$.},

author = {Ra'ed, Hatamleh},

journal = {Archivum Mathematicum},

keywords = {commutative nonstationary stochastic fields; correlation function; infinitesimal correlation function; contractive semigroup; correlation function; infinitesimal correlation function; contractive semigroup},

language = {eng},

number = {3},

pages = {161-169},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Commutative nonstationary stochastic fields},

url = {http://eudml.org/doc/248951},

volume = {038},

year = {2002},

}

TY - JOUR

AU - Ra'ed, Hatamleh

TI - Commutative nonstationary stochastic fields

JO - Archivum Mathematicum

PY - 2002

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 038

IS - 3

SP - 161

EP - 169

AB - 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: $T_t (\varepsilon )=\exp (it A_{\varepsilon })$, $A_\varepsilon = A_1 +\varepsilon A_2$, $|\varepsilon | \ll 1$.

LA - eng

KW - commutative nonstationary stochastic fields; correlation function; infinitesimal correlation function; contractive semigroup; correlation function; infinitesimal correlation function; contractive semigroup

UR - http://eudml.org/doc/248951

ER -

## References

top- Higher transcendental functions, McGraw-Hill, New York 1953. Zbl0542.33002
- On a certain class of non-stationary random processes, Teor. Funkts., Funkts. Anal. Prilozh., Kharkov 14 (1971), 150–160 (Russian).
- Linear representable random processes, God. Sofij. Univ., Mat. Fak. 66 (1974), 287–306 (Russian).
- Nonstationary curves in Hilbert spaces and their correlation functions I, Integral Equations Operator Theory 19 (1994), 270–289. MR1280124
- Nonstationary curves in Hilbert spaces and their correlation functions II, Integral Equations Operator Theory 19 (1994), 447–457. MR1285492
- Theory of operator colligation in Hilbert space, Engl. transl. J. Wiley, N.Y. 1979. MR0634097
- On open systems and characteristic functions of commuting operator systems, VINITI 857-79, 1-37 (Russian).

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