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Mean square stability of stochastic Volterra integro-differential equations. (English) Zbl 1129.34332

Summary: The mean square stability of a non-linear stochastic Volterra integro-differential equation is studied. Non-convolution Volterra terms arise in both the drift and the dispersion term. Moreover, for the convolution case we determine the rate of convergence in terms of an integrability condition on the Volterra kernels.

MSC:

34K20 Stability theory of functional-differential equations
34K50 Stochastic functional-differential equations
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
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