Title: Mean square characterisation of a stochastic Volterra integrodifferential equation with delay

Authors: John A.D. Appleby

Addresses: School of Mathematical Sciences, Dublin City University, Dublin 9, Ireland

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.

Keywords: stochastic functional differential equations; stochastic Volterra equation; mean square stability; characteristic equation; characteristic exponent; renewal equation; exponential stability; variation of constants formula.

DOI: 10.1504/IJDSDE.2021.117374

International Journal of Dynamical Systems and Differential Equations, 2021 Vol.11 No.3/4, pp.194 - 226

Received: 01 Jul 2020
Accepted: 02 Mar 2021
Published online: 01 Sep 2021 *

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