Polynomial asymptotic stability of damped stochastic differential equations.

Appleby, John A.D.; Mackey, Dana

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The paper discusses the asymptotic properties of solutions of the scalar functional differential equation $y^{'} (x) = a y (τ (x)) + b y (x), x \in [x_{0}, \infty]$ . Asymptotic formulas are given in terms of solutions of the appropriate scalar functional nondifferential equation.