Commutative nonstationary stochastic fields

Hatamleh Ra'ed

Archivum Mathematicum (2002)

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

Abstract

top
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 ( ε ) = exp ( i t A ε ) , A ε = A 1 + ε A 2 , | ε | ≪ 1 .

How to cite

top

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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.