38 citations · 117 across the 22 of their papers we have counts for
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On the Dynamic Consistency of the Split Step Method for Classifying the Asymptotic Behaviour of Globally Stable Differential Equations perturbed by State--independent Stochastic terms
John A. D. Appleby, Jian Cheng, Alexandra Rodkina
In this paper we classify the pathwise asymptotic behaviour of the discretisation of a general autonomous scalar differential equation which has a unique and globally stable equili…
Exact growth rates of solutions of delay--dominated differential equations with regularly varying coefficients
John A. D. Appleby, Michael J. McCarthy, Alexandra Rodkina
In this paper we determine the exact rate of growth of the solution of a deterministic delay differential equation in which the delayed term is regularly varying at infinity and do…
Classification of the Asymptotic Behaviour of Globally Stable Differential Equations with Respect to State-independent Stochastic Perturbations
John A. D. Appleby, Jian Cheng, Alexandra Rodkina
In this paper we consider the global stability of solutions of a nonlinear stochastic differential equation. The differential equation is a perturbed version of a globally stable l…
Classification of the Asymptotic Behaviour of Globally Stable Linear Differential Equations with Respect to State-independent Stochastic Perturbations
John A. D. Appleby, Jian Cheng, Alexandra Rodkina
In this paper we consider the global stability of solutions of an affine stochastic differential equation. The differential equation is a perturbed version of a globally stable lin…
On the Classification of the Asymptotic Behaviour of Solutions of Globally Stable Scalar Differential Equations with Respect to State--Independent Stochastic Perturbations
John A. D. Appleby, Jian Cheng, Alexandra Rodkina
In this paper we characterise the global stability, global boundedness and recurrence of solutions of a scalar nonlinear stochastic differential equation. The differential equation…
On limit periodicity of discrete time stochastic processes
Alexandra Rodkina, Nikolai Dokuchaev, John Appleby
We consider a discrete time dynamic system described by a difference equation with periodic coefficients and with additive stochastic noise. We investigate the possibility of the p…