Previous |  Up |  Next


Title: Asymptotic normality of eigenvalues of random ordinary differential operators (English)
Author: Hála, Martin
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940
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
Date available: 2008-05-20T18:41:53Z
Last updated: 2015-05-28
Stable URL:
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
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
Reference: [10] F. Rellich: Störungsrechnung der Spektralzerlegung - IV. Mitteilung.Math. Ann, 117 (1940), 356-382. MR 0002715
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).


Files Size Format View
AplMat_36-1991-4_2.pdf 1.304Mb application/pdf View/Open
Back to standard record
Partner of
EuDML logo