3 papers
math.CA2025
Critical perturbation sizes for preserving decay rates in solutions of perturbed nonlinear differential equations
John A. D. Appleby, Subham Pal
This paper develops necessary and sufficient conditions for the preservation of asymptotic convergence rates of deterministically and stochastically perturbed ordinary differential…
math.CA2024
Weighted Asymptotic Characterisation of Perturbed Autonomous Linear Ordinary and Stochastic Differential Equations: Part I -- ODEs
John A. D. Appleby, Emmet Lawless
This is the first of a two-part paper which determines necessary and sufficient conditions on the asymptotic behaviour of forcing functions so that the solutions of additively pert…
math.CA2024
Characterisation of asymptotic behaviour of perturbed deterministic and stochastic pantograph equations
John A. D. Appleby, Emmet Lawless
This paper considers the asymptotic behaviour of deterministically and stochastically forced linear pantograph equations. The asymptotic behaviour is studied in the case when all s…