Theory of Probability and Mathematical Statistics
Bounded in the mean and stationary solutions of second-order difference equations with operator coefficients
M.F. Horodnii
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Abstract: We study the question of the existence of a unique bounded in the mean solution for the second-order difference equation with piecewise constant operator coefficients and of the stationary solution of the corresponding difference equation with constant operator coefficients. The case is considered when the corresponding “algebraic” operator equations have separated roots.
Keywords: Banach space, second-order difference equation, bounded in the mean solution, stationary solution, “algebraic” operator equation, separated roots
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