On the admissibility of unboundedness properties of forced deterministic and stochastic sublinear Volterra summation equations

@article{Appleby2016OnTA,
  title={On the admissibility of unboundedness properties of forced deterministic and stochastic sublinear Volterra summation equations},
  author={J. Appleby and Denis D. Patterson},
  journal={arXiv: Dynamical Systems},
  year={2016}
}
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--dependence in the summation is of smaller than linear order for large absolute values of the state. When the perturbation term is unbounded, it is elementary to show that solutions are also. The main results of the paper are mostly of the following form: the solution has an additional unboundedness property $U$ if… Expand
Large fluctuations and growth rates of linear Volterra summation equations
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 is summable andExpand

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