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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)
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