20 citations · 36 across the 9 of their papers we have counts for
12 papers
On splitting strategies for the numerical solution of stochastic delay differential equations with correlated noises
Cónall Kelly, Wenshi Tang
In this article we investigate the numerical solution of a scalar semilinear stochastic delay differential equation (SDDE) where the linear instantaneous feedback and nonlinear del…
Adaptive Mesh Construction for the Numerical Solution of Stochastic Differential Equations with Markovian Switching
Cónall Kelly, Kate O'Donovan
We demonstrate an approach to the numerical solution of nonlinear stochastic differential equations with Markovian switching. Such equations describe the stochastic dynamics of pro…
An adaptive splitting method for the Cox-Ingersoll-Ross process
Cónall Kelly, Gabriel J. Lord
We propose a new splitting method for strong numerical solution of the Cox-Ingersoll-Ross model. For this method, applied over both deterministic and adaptive random meshes, we pro…
Stabilization of cycles with stochastic prediction-based and target-oriented control
Elena Braverman, Conall Kelly, Alexandra Rodkina
We stabilize a prescribed cycle or an equilibrium of the difference equation using pulsed stochastic control. Our technique, inspired by the Kolmogorov's Law of Large Numbers, acti…
The role of adaptivity in a numerical method for the Cox-Ingersoll-Ross model
Cónall Kelly, Gabriel Lord, Heru Maulana
We demonstrate the effectiveness of an adaptive explicit Euler method for the approximate solution of the Cox-Ingersoll-Ross model. This relies on a class of path-bounded timestepp…
Strong convergence of an adaptive time-stepping Milstein method for SDEs with monotone coefficients
Cónall Kelly, Gabriel Lord, Fandi Sun
We introduce an explicit adaptive Milstein method for stochastic differential equations (SDEs) with no commutativity condition. The drift and diffusion are separately locally Lipsc…
Adaptive Euler methods for stochastic systems with non-globally Lipschitz coefficients
Cónall Kelly, Gabriel Lord
We present strongly convergent explicit and semi-implicit adaptive numerical schemes for systems of stiff stochastic differential equations (SDEs) where both the drift and diffusio…
On cubic difference equations with variable coefficients and fading stochastic perturbations
Ricardo Baccas, Cónall Kelly, Alexandra Rodkina
We consider the stochastically perturbed cubic difference equation with variable coefficients \[ x_{n+1}=x_n(1-h_nx_n^2)+ρ_{n+1}ξ_{n+1}, \quad n\in \mathbb N,\quad x_0\in \mathbb R…
Adaptive timestepping for pathwise stability and positivity of strongly discretised nonlinear stochastic differential equations
Cónall Kelly, Alexandra Rodkina, Eeva Maria Rapoo
We consider the use of adaptive timestepping to allow a strong explicit Euler-Maruyama discretisation to reproduce dynamical properties of a class of nonlinear stochastic different…
Adaptive timestepping strategies for nonlinear stochastic systems
Cónall Kelly, Gabriel J. Lord
We introduce a class of adaptive timestepping strategies for stochastic differential equations with non-Lipschitz drift coefficients. These strategies work by controlling potential…
Stochastic stability analysis of a reduced galactic dynamo model with perturbed α-effect
Cónall Kelly
We investigate the asymptotic behaviour of a reduced αΩ-dynamo model of magnetic field generation in spiral galaxies where fluctuation in the α-effect results in a system with stat…
Stabilisation of difference equations with noisy prediction-based control
Elena Braverman, Conall Kelly, Alexandra Rodkina
We consider the influence of stochastic perturbations on stability of a unique positive equilibrium of a difference equation subject to prediction-based control. These perturbation…