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Exponential stability in mean square of neutral stochastic differential functional equations. (English) Zbl 0877.93133
Summary: The aim of this paper is to investigate the exponential stability in mean square for a neutral stochastic differential functional equation of the form $$d[x(t)-G(x_{t})]=[f(t,x(t))+g(t,x_{t})]dt+\sigma (t,x_{t})dw(t),$$ where $x_{t}={x(t+s):-\tau \le s\le 0}$, with $\tau >0$, is the past history of the solution. Several interesting examples are also given for illustration.

93E15Stochastic stability
34K50Stochastic functional-differential equations
Full Text: DOI
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