| Title:
|
Commutative nonstationary stochastic fields (English) |
| Author:
|
Ra'ed, Hatamleh |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
38 |
| Issue:
|
3 |
| Year:
|
2002 |
| Pages:
|
161-169 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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: $T_t (\varepsilon )=\exp (it A_{\varepsilon })$, $A_\varepsilon = A_1 +\varepsilon A_2$, $|\varepsilon | \ll 1$. (English) |
| Keyword:
|
commutative nonstationary stochastic fields |
| Keyword:
|
correlation function |
| Keyword:
|
infinitesimal correlation function |
| Keyword:
|
contractive semigroup |
| MSC:
|
47D99 |
| MSC:
|
47N30 |
| MSC:
|
60G12 |
| idZBL:
|
Zbl 1068.60051 |
| idMR:
|
MR1921588 |
| . |
| Date available:
|
2008-06-06T22:30:17Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107830 |
| . |
| Reference:
|
[1] Erdelyi, A. (ed.): Higher transcendental functions.McGraw-Hill, New York 1953. Zbl 0542.33002 |
| Reference:
|
[2] Kirchev, K. P.: On a certain class of non-stationary random processes.Teor. Funkts., Funkts. Anal. Prilozh., Kharkov 14 (1971), 150–160 (Russian). |
| Reference:
|
[3] Kirchev, K. P.: Linear representable random processes.God. Sofij. Univ., Mat. Fak. 66 (1974), 287–306 (Russian). |
| Reference:
|
[4] Kirchev, K. P., Zolotarev, V. A.: Nonstationary curves in Hilbert spaces and their correlation functions I.Integral Equations Operator Theory 19 (1994), 270–289. MR 1280124 |
| Reference:
|
[5] Kirchev, K. P., Zolotarev, V. A.: Nonstationary curves in Hilbert spaces and their correlation functions II.Integral Equations Operator Theory 19 (1994), 447–457. MR 1285492 |
| Reference:
|
[6] Livshits, M. S., Yantsevich, A. A.: Theory of operator colligation in Hilbert space.Engl. transl. J. Wiley, N.Y. 1979. MR 0634097 |
| Reference:
|
[7] Zolotarev, V. A.: On open systems and characteristic functions of commuting operator systems.VINITI 857-79, 1-37 (Russian). |
| . |
