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math.DS2016★ 3 cited
Large fluctuations and growth rates of linear Volterra summation equations
John A. D. Appleby, Denis D. Patterson
This paper concerns the asymptotic behaviour of solutions of a linear convolution Volterra summation equation with an unbounded forcing term. In particular, we suppose the kernel i…
math.DS2016
On the admissibility of unboundedness properties of forced deterministic and stochastic sublinear Volterra summation equations
John A. D. Appleby, Denis D. Patterson
In this paper we consider unbounded solutions of perturbed convolution Volterra summation equations. The equations studied are asymptotically sublinear, in the sense that the state…