## Asymptotic properties of neutral stochastic differential delay equations.(English)Zbl 0964.60066

The author considers neutral stochastic differential delay equations of the form $d[x(t)-G(x(t-\tau))] =f( x(t),x(t-\tau),t) dt +g( x(t),x(t-\tau),t) dB(t).$ Using the new techniques developed in the paper, the author investigates the moment and almost sure exponential stability and gives a unified treatment for various asymptotic estimates, e.g., asymptotic exponential and polynomial bounds for the solution.

### MSC:

 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)

### Keywords:

asymptotic stability; Lyapunov function; Itô formula
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### References:

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