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.
@article{104465, author = {Martin H\'ala}, title = {Asymptotic normality of eigenvalues of random ordinary differential operators}, journal = {Applications of Mathematics}, volume = {36}, year = {1991}, pages = {264-276}, zbl = {0737.60056}, mrnumber = {1113950}, language = {en}, url = {http://dml.mathdoc.fr/item/104465} }
Hála, Martin. Asymptotic normality of eigenvalues of random ordinary differential operators. Applications of Mathematics, Tome 36 (1991) pp. 264-276. http://gdmltest.u-ga.fr/item/104465/
Technische Dynamik, Springer-Verlag, Berlin, 1939. (1939)
Eigenwertaufgaben mit technischen Anwendungen, Geest & Portig, Leipzig, 1963. (1963) | MR 0152101
Perturbation theory, (Russian). Mir, Moskva, 1972. (1972) | Zbl 0247.47009
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). (1981)
Stochastic Dynamic Models, Academia, Prague, 1985 (in Czech). (1985) | MR 0819740
Stochastic Integrals, Academic Press, New York-London, 1969. (1969) | MR 0247684
Störungsrechnung der Spektralzerlegung - I. Mitteilung, Math. Ann. 113 (1937), 600-619. (1937) | MR 1513109
Störungsrechnung der Spektralzerlegung - II. Mitteilung, Math. Ann. 113 (1937), 685-698. (1937)
Störungsrechnung der Spektralzerlegung - III. Mitteilung, Math. Ann. 116 (1939), 555-570. (1939) | MR 1513244
Störungsrechnung der Spektralzerlegung - IV. Mitteilung, Math. Ann, 117 (1940), 356-382. (1940) | MR 0002715
Stationary stochastic processes, (Russian). Fizmatgiz, Moskva, 1963. (1963) | MR 0159363
Random Eigenvalue Problems, Akademie-Verlag, Berlin, 1983. (1983) | MR 0790850
The distribution of natural frequencies of some basic supporting engineering structures made of reinforced concrete, VUT Brno, 1987 (dissertation - in Czech). (1987)