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Stability of stochastic integro-differential equations. (English) Zbl 0969.60068

Theorems giving conditions under which vector nonlinear stochastic integro-differential equations of the form \[ dx(t)= f\bigl(x(t), t \bigr)dt+ g\left(\int^t_0 G(t-s)x(s) ds,t\right) dw(t) \] are exponentially stable in the mean square and under which they are \(L^2\)-stable are proved. An example is given to illustrate the application of these theorems to a specific equation.

MSC:

60H99 Stochastic analysis
45J05 Integro-ordinary differential equations
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