Asymptotic normality of eigenvalues of random ordinary differential operators

Martin Hála

Applications of Mathematics (1991)

  • Volume: 36, Issue: 4, page 264-276
  • ISSN: 0862-7940

Abstract

top
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.

How to cite

top

Hála, Martin. "Asymptotic normality of eigenvalues of random ordinary differential operators." Applications of Mathematics 36.4 (1991): 264-276. <http://eudml.org/doc/15678>.

@article{Hála1991,
abstract = {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.},
author = {Hála, Martin},
journal = {Applications of Mathematics},
keywords = {ordinary differential operators; random coefficient processes; asymptotic normality of eigenvalues; ordinary differential equations with random coefficients; asymptotic normality of eigenvalues},
language = {eng},
number = {4},
pages = {264-276},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Asymptotic normality of eigenvalues of random ordinary differential operators},
url = {http://eudml.org/doc/15678},
volume = {36},
year = {1991},
}

TY - JOUR
AU - Hála, Martin
TI - Asymptotic normality of eigenvalues of random ordinary differential operators
JO - Applications of Mathematics
PY - 1991
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 36
IS - 4
SP - 264
EP - 276
AB - 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.
LA - eng
KW - ordinary differential operators; random coefficient processes; asymptotic normality of eigenvalues; ordinary differential equations with random coefficients; asymptotic normality of eigenvalues
UR - http://eudml.org/doc/15678
ER -

References

top
  1. C. B. Biezeno R. Grammel, Technische Dynamik, Springer-Verlag, Berlin, 1939. (1939) 
  2. L. Collatz, Eigenwertaufgaben mit technischen Anwendungen, Geest & Portig, Leipzig, 1963. (1963) MR0152101
  3. T. Kato, Perturbation theory, (Russian). Mir, Moskva, 1972. (1972) Zbl0247.47009
  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). (1981) 
  5. P. Mandl, Stochastic Dynamic Models, Academia, Prague, 1985 (in Czech). (1985) MR0819740
  6. H. P. Mc Kean, Jr., Stochastic Integrals, Academic Press, New York-London, 1969. (1969) MR0247684
  7. F. Rellich, 10.1007/BF01571652, Math. Ann. 113 (1937), 600-619. (1937) MR1513109DOI10.1007/BF01571652
  8. F. Rellich, Störungsrechnung der Spektralzerlegung - II. Mitteilung, Math. Ann. 113 (1937), 685-698. (1937) 
  9. F. Rellich, 10.1007/BF01597374, Math. Ann. 116 (1939), 555-570. (1939) MR1513244DOI10.1007/BF01597374
  10. F. Rellich, 10.1007/BF01450023, Math. Ann, 117 (1940), 356-382. (1940) MR0002715DOI10.1007/BF01450023
  11. J. A. Rozanov, Stationary stochastic processes, (Russian). Fizmatgiz, Moskva, 1963. (1963) MR0159363
  12. J. V. Scheidt W. Purkert, Random Eigenvalue Problems, Akademie-Verlag, Berlin, 1983. (1983) MR0790850
  13. M. Šikulová, The distribution of natural frequencies of some basic supporting engineering structures made of reinforced concrete, VUT Brno, 1987 (dissertation - in Czech). (1987) 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.