38 citations · 70 across the 29 of their papers we have counts for
12 papers · 1 filter
Mean square asymptotic stability characterisation of perturbed linear stochastic functional differential equations
John Appleby, Emmet Lawless
In this paper we investigate the mean square asymptotic stability of a perturbed scalar linear stochastic functional differential equation. Specifically, we are able to give necess…
Recurrent Solutions of Stochastic Differential Equations with Non-constant Diffusion Coefficients which obey the Law of the Iterated Logarithm
John A. D. Appleby, Huizhong Appleby-Wu
By using a change of scale and space, we study a class of stochastic differential equations (SDEs) whose solutions are drift--perturbed and exhibit behaviour analogous to standard…
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…
On the Existence and Uniqueness of Solutions of Stochastic Equations of Neutral Type
John A. D. Appleby, Huizhong Appleby-Wu, Xuerong Mao
This paper considers some the existence and uniqueness of strong solutions of stochastic neutral functional differential equations. The conditions on the neutral functional relax t…
On the almost sure running maxima of solutions of affine neutral stochastic functional differential equations
John A. D. Appleby, Huizhong Appleby-Wu, Xuerong Mao
This paper studies the large fluctuations of solutions of finite--dimensional affine stochastic neutral functional differential equations with finite memory, as well as related non…
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…