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Theory of Probability and Mathematical Statistics

ISSN 1547-7363(online) ISSN 0094-9000(print)



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

Author: M. F. Horodnii
Journal: Theor. Probability and Math. Statist. 106 (2022), 177-181
MSC (2020): Primary 60H99; Secondary 34G10
Published electronically: May 16, 2022
MathSciNet review: 4438450
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Abstract | References | Similar Articles | Additional Information

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.

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Additional Information

M. F. Horodnii
Affiliation: Taras Shevchenko National University of Kyiv, 64, Volodymyrs’ka St., 01601 Kyiv, Ukraine

Keywords: Banach space, second-order differential equation, stationary solution, “algebraic” operator equation, separated roots
Received by editor(s): January 5, 2022
Accepted for publication: January 24, 2022
Published electronically: May 16, 2022
Additional Notes: This work has been supported by Ministry of Education and Science of Ukraine: Grant of the Ministry of Education and Science of Ukraine for perspective development of a scientific direction “Mathematical sciences and natural sciences” at Taras Shevchenko National University of Kyiv.
Article copyright: © Copyright 2022 Taras Shevchenko National University of Kyiv