| Title:
|
Asymptotic normality of eigenvalues of random ordinary differential operators (English) |
| Author:
|
Hála, Martin |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
36 |
| Issue:
|
4 |
| Year:
|
1991 |
| Pages:
|
264-276 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Boundary value problems for ordinary differential equations with random coefficients are dealt with. The coefficients are assumed to be Gaussian vectorial stationary processes multiplied by intensity functions and converging to the white noise process. A theorem on the limit distribution of the random eigenvalues is presented together with applications in mechanics and dynamics. (English) |
| Keyword:
|
ordinary differential operators |
| Keyword:
|
random coefficient processes |
| Keyword:
|
asymptotic normality of eigenvalues |
| MSC:
|
34B05 |
| MSC:
|
34F05 |
| MSC:
|
34L10 |
| MSC:
|
34L40 |
| MSC:
|
60H25 |
| MSC:
|
73H05 |
| idZBL:
|
Zbl 0737.60056 |
| idMR:
|
MR1113950 |
| DOI:
|
10.21136/AM.1991.104465 |
| . |
| Date available:
|
2008-05-20T18:41:53Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104465 |
| . |
| Reference:
|
[1] C. B. Biezeno R. Grammel: Technische Dynamik.Springer-Verlag, Berlin, 1939. |
| Reference:
|
[2] L. Collatz: Eigenwertaufgaben mit technischen Anwendungen.Geest & Portig, Leipzig, 1963. MR 0152101 |
| Reference:
|
[3] T. Kato: Perturbation theory.(Russian). Mir, Moskva, 1972. Zbl 0247.47009 |
| Reference:
|
[4] V. Lánská: The process from representation by means of spectral density to the representation by means of stochastic differential equations.ÚTIA-ČSAV, Prague, 1981 (Research Report No. 1094 - in Czech). |
| Reference:
|
[5] P. Mandl: Stochastic Dynamic Models.Academia, Prague, 1985 (in Czech). MR 0819740 |
| Reference:
|
[6] H. P. Mc Kean, Jr.: Stochastic Integrals.Academic Press, New York-London, 1969. MR 0247684 |
| Reference:
|
[7] F. Rellich: Störungsrechnung der Spektralzerlegung - I. Mitteilung.Math. Ann. 113 (1937), 600-619. MR 1513109, 10.1007/BF01571652 |
| Reference:
|
[8] F. Rellich: Störungsrechnung der Spektralzerlegung - II. Mitteilung.Math. Ann. 113 (1937), 685-698. |
| Reference:
|
[9] F. Rellich: Störungsrechnung der Spektralzerlegung - III. Mitteilung.Math. Ann. 116 (1939), 555-570. MR 1513244, 10.1007/BF01597374 |
| Reference:
|
[10] F. Rellich: Störungsrechnung der Spektralzerlegung - IV. Mitteilung.Math. Ann, 117 (1940), 356-382. MR 0002715, 10.1007/BF01450023 |
| Reference:
|
[11] J. A. Rozanov: Stationary stochastic processes.(Russian). Fizmatgiz, Moskva, 1963. MR 0159363 |
| Reference:
|
[12] J. V. Scheidt W. Purkert: Random Eigenvalue Problems.Akademie-Verlag, Berlin, 1983. MR 0790850 |
| Reference:
|
[13] M. Šikulová: The distribution of natural frequencies of some basic supporting engineering structures made of reinforced concrete.VUT Brno, 1987 (dissertation - in Czech). |
| . |
