Geodesic
Asymptotic normality of eigenvalues of random ordinary differential operators
Applications of Mathematics, Tome 36 (1991) no. 4, pp. 264-276

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
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.
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.
DOI : 10.21136/AM.1991.104465
Classification : 34B05, 34F05, 34L10, 34L40, 60H25, 73H05
Keywords: ordinary differential operators; random coefficient processes; asymptotic normality of eigenvalues 
Hála, Martin. Asymptotic normality of eigenvalues of random ordinary differential operators. Applications of Mathematics, Tome 36 (1991) no. 4, pp. 264-276. doi: 10.21136/AM.1991.104465
@article{10_21136_AM_1991_104465,
     author = {H\'ala, Martin},
     title = {Asymptotic normality of eigenvalues of random ordinary differential operators},
     journal = {Applications of Mathematics},
     pages = {264--276},
     year = {1991},
     volume = {36},
     number = {4},
     doi = {10.21136/AM.1991.104465},
     mrnumber = {1113950},
     zbl = {0737.60056},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1991.104465/}
}
TY  - JOUR
AU  - Hála, Martin
TI  - Asymptotic normality of eigenvalues of random ordinary differential operators
JO  - Applications of Mathematics
PY  - 1991
SP  - 264
EP  - 276
VL  - 36
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1991.104465/
DO  - 10.21136/AM.1991.104465
LA  - en
ID  - 10_21136_AM_1991_104465
ER  - 
%0 Journal Article
%A Hála, Martin
%T Asymptotic normality of eigenvalues of random ordinary differential operators
%J Applications of Mathematics
%D 1991
%P 264-276
%V 36
%N 4
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1991.104465/
%R 10.21136/AM.1991.104465
%G en
%F 10_21136_AM_1991_104465

[1] C. B. Biezeno R. Grammel: Technische Dynamik. Springer-Verlag, Berlin, 1939.

[2] L. Collatz: Eigenwertaufgaben mit technischen Anwendungen. Geest & Portig, Leipzig, 1963. | MR

[3] T. Kato: Perturbation theory. (Russian). Mir, Moskva, 1972. | Zbl

[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).

[5] P. Mandl: Stochastic Dynamic Models. Academia, Prague, 1985 (in Czech). | MR

[6] H. P. Mc Kean, Jr.: Stochastic Integrals. Academic Press, New York-London, 1969. | MR

[7] F. Rellich: Störungsrechnung der Spektralzerlegung - I. Mitteilung. Math. Ann. 113 (1937), 600-619. | DOI | MR

[8] F. Rellich: Störungsrechnung der Spektralzerlegung - II. Mitteilung. Math. Ann. 113 (1937), 685-698.

[9] F. Rellich: Störungsrechnung der Spektralzerlegung - III. Mitteilung. Math. Ann. 116 (1939), 555-570. | DOI | MR

[10] F. Rellich: Störungsrechnung der Spektralzerlegung - IV. Mitteilung. Math. Ann, 117 (1940), 356-382. | DOI | MR

[11] J. A. Rozanov: Stationary stochastic processes. (Russian). Fizmatgiz, Moskva, 1963. | MR

[12] J. V. Scheidt W. Purkert: Random Eigenvalue Problems. Akademie-Verlag, Berlin, 1983. | MR

[13] M. Šikulová: The distribution of natural frequencies of some basic supporting engineering structures made of reinforced concrete. VUT Brno, 1987 (dissertation - in Czech).

Cité par Sources :