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

  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},
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
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