Stationary solutions of a second-order differential equation with operator coefficients

Author:

Horodnii M.

Abstract

Necessary and sufficient conditions are given for the existence of a unique stationary solution to the second-order linear differential equation with bounded operator coefficients, perturbed by a stationary process. In the case when the corresponding “algebraic” operator equation has separated roots, the new representation of the stationary solution of the considered differential equation is obtained.

Publisher

American Mathematical Society (AMS)

Subject

Statistics, Probability and Uncertainty,Statistics and Probability

Reference7 articles.

1. On stability of motion for random disturbances;Vorovič, I. I.;Izv. Akad. Nauk SSSR. Ser. Mat.,1956

2. Some remarks on differential equations perturbed by periodic random processes;Dorogovcev, A. Ja.;Ukrain. Mat. \v{Z}.,1962

3. R. Z. Khas’minskii, Stability of Systems of Differential Equations under Random Perturbations of Their Parameters, “Nauka”, Moscow, Sijthoff and Noordhoff, Alphen aan Rijn, 1980.

4. Periodic solutions of evolution differential equations that are perturbed by stochastic processes;Dorogovtsev, A. Ya.;Ukrain. Mat. Zh.,1989

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