# 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}
}```
• Published 2016
• Mathematics
• 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
1 Citations
Large fluctuations and growth rates of linear Volterra summation equations
• Mathematics
• 2016
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

#### References

SHOWING 1-10 OF 40 REFERENCES
On the boundedness of the solutions in nonlinear discrete Volterra difference equations
• Mathematics
• 2012
In this article, we investigate the boundedness property of the solutions of linear and nonlinear discrete Volterra equations in both convolution and non-convolution case. Strong interest in theseExpand
On exact convergence rates for solutions of linear systems of Volterra difference equations
• Mathematics
• 2006
The asymptotic behaviour of the solution of general linear Volterra non-convolution difference equations on a finite dimensional space, is investigated. It is proved under appropriate assumptionsExpand
Long Memory in a Linear Stochastic Volterra Differential Equation
• Mathematics
• 2010
In this paper we consider a linear stochastic Volterra equation which has a stationary solution. We show that when the kernel of the fundamental solution is regularly varying at infinity with aExpand
On Regularly Varying and History-Dependent Convergence Rates of Solutions of a Volterra Equation with Infinite Memory
We consider the rate of convergence to equilibrium of Volterra integrodifferential equations with infinite memory. We show that if the kernel of Volterra operator is regularly varying at infinity,Expand
On admissibility of the resolvent of discrete Volterra equations
• Mathematics
• 2010
Suppose that a pair of sequence spaces is admissible with respect to a discrete linear Volterra operator. This paper gives sufficient conditions for the same pair of spaces to be admissible withExpand
Linearized stability analysis of discrete Volterra equations
• Mathematics
• 2004
Abstract Various different types of stability are defined, in a unified framework, for discrete Volterra equations of the type x ( n )= f ( n )+∑ n j =0 K ( n , j , x ( n )) ( n ⩾0). UnderExpand
Asymptotic Representation of the Solutions of Linear Volterra Difference Equations
• Mathematics
• 2008
This article analyses the asymptotic behaviour of solutions of linear Volterra difference equations. Some sufficient conditions are presented under which the solutions to a general linear equationExpand