Theory of Probability and Mathematical Statistics
Stationary solutions of a second-order differential equation with operator coefficients
M. F. Horodnii
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.
Keywords: Banach space, second-order differential equation, stationary solution, “algebraic” operator equation, separated roots
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