Zobrazeno 1 - 10
of 43
pro vyhledávání: '"Kelly, Conall"'
Autor:
Kelly, Cónall, O'Donovan, Kate
We demonstrate an approach to the numerical solution of nonlinear stochastic differential equations with Markovian switching. Such equations describe the stochastic dynamics of processes where the drift and diffusion coefficients are subject to rando
Externí odkaz:
http://arxiv.org/abs/2408.14931
We develop adaptive time-stepping strategies for It\^o-type stochastic differential equations (SDEs) with jump perturbations. Our approach builds on adaptive strategies for SDEs. Adaptive methods can ensure strong convergence of nonlinear SDEs with d
Externí odkaz:
http://arxiv.org/abs/2312.06910
Autor:
Kelly, Cónall, Lord, Gabriel J.
Publikováno v:
Applied Numerical Mathematics, Volume 186, 2023, Pages 252-273
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 prove a uniform moment bound and strong error results of order $1/4$ in $
Externí odkaz:
http://arxiv.org/abs/2112.09465
Publikováno v:
Chaos, V. 30 (2020), 15 pp
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, activates a stabilizing effect of stochastic perturbation and allows for s
Externí odkaz:
http://arxiv.org/abs/2012.11086
Publikováno v:
In Mathematics and Computers in Simulation January 2025 227:461-476
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 timestepping strategies which work by reducing the stepsize as solutions approa
Externí odkaz:
http://arxiv.org/abs/2002.10206
We introduce an explicit adaptive Milstein method for stochastic differential equations (SDEs) with no commutativity condition. The drift and diffusion are separately locally Lipschitz and together satisfy a monotone condition. This method relies on
Externí odkaz:
http://arxiv.org/abs/1909.00099
Autor:
Kelly, Cónall, Lord, Gabriel J.
Publikováno v:
In Applied Numerical Mathematics April 2023 186:252-273
Autor:
Kelly, Cónall, Lord, Gabriel
We present strongly convergent explicit and semi-implicit adaptive numerical schemes for systems of stiff stochastic differential equations (SDEs) where both the drift and diffusion are non-globally Lipschitz continuous. This stiffness may originate
Externí odkaz:
http://arxiv.org/abs/1805.11137
We consider the stochastically perturbed cubic difference equation with variable coefficients \[ x_{n+1}=x_n(1-h_nx_n^2)+\rho_{n+1}\xi_{n+1}, \quad n\in \mathbb N,\quad x_0\in \mathbb R. \] Here $(\xi_n)_{n\in \mathbb N}$ is a sequence of independent
Externí odkaz:
http://arxiv.org/abs/1802.01350