John A. D. Appleby

activity

20242026

collaborators

5 papers

math.DS2026

Solution space characterisation of perturbed linear discrete and continuous stochastic Volterra convolution equations: the $ℓ^{p}$ and $L^{p}$ cases

John A. D. Appleby, Emmet Lawless

In this article, we are concerned with characterising when solutions of perturbed linear stochastic Volterra summation equations are almost surely $p$ -summable and when their conti…

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.CA2025

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…

math.CA2024

Solution space characterisation of perturbed linear functional and integrodifferential Volterra convolution equations: CesÃ ro limits

John A. D. Appleby, Emmet Lawless

In this article we discuss the requirements needed in order to characterise the solution space of perturbed linear integro-differential Volterra convolution equations. We highlight…

math.CA2024

Weighted $L_{\infty}$ 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…

Solution space characterisation of perturbed linear discrete and continuous stochastic Volterra convolution equations: the ℓp and Lp cases

Critical perturbation sizes for preserving decay rates in solutions of perturbed nonlinear differential equations

Characterisation of asymptotic behaviour of perturbed deterministic and stochastic pantograph equations

Solution space characterisation of perturbed linear functional and integrodifferential Volterra convolution equations: CesÃ ro limits

Weighted L∞​ Asymptotic Characterisation of Perturbed Autonomous Linear Ordinary and Stochastic Differential Equations: Part I -- ODEs

Solution space characterisation of perturbed linear discrete and continuous stochastic Volterra convolution equations: the $ℓ^{p}$ and $L^{p}$ cases

Weighted $L_{\infty}$ Asymptotic Characterisation of Perturbed Autonomous Linear Ordinary and Stochastic Differential Equations: Part I -- ODEs