Mean square characterisation of a stochastic Volterra integrodifferential equation with delay
by John A.D. Appleby
International Journal of Dynamical Systems and Differential Equations (IJDSDE), Vol. 11, No. 3/4, 2021

Abstract: In this paper the asymptotic behaviour of the mean square of the solution of a linear stochastic Volterra integro-differential equation with delay is entirely characterised. In the case when the solution is mean-square asymptotically stable or unstable the exact rate of growth or decay can be determined by the real solution of a transcendental equation which is constructed as a by-product of the proof. The proof of the mean square stability of an equation with fading memory is also sketched.

Online publication date: Wed, 01-Sep-2021

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