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…
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…
Non-exponential stability and decay rates in nonlinear stochastic difference equation with unbounded noises
J. A. D. Appleby, G. Berkolaiko, A. Rodkina
We consider stochastic difference equation x_{n+1} = x_n (1 - h f(x_n) + \sqrt{h} g(x_n) ξ_{n+1}), where functions f and g are nonlinear and bounded, random variables ξ_i are indep…
Almost Sure Convergence of Solutions to Non-Homogeneous Stochastic Difference Equation
Gregory Berkolaiko, Alexandra Rodkina
We consider a non-homogeneous nonlinear stochastic difference equation X_{n+1} = X_n (1 + f(X_n)ξ_{n+1}) + S_n, and its important special case X_{n+1} = X_n (1 + ξ_{n+1}) + S_n, bo…