155 citations · 231 across the 10 of their papers we have counts for
10 papers
Generative Modelling of Lévy Area for High Order SDE Simulation
Andraž Jelinčič, Jiajie Tao, William F. Turner +3
It is well understood that, when numerically simulating SDEs with general noise, achieving a strong convergence rate better than (where h is the step size) requires t…
High order splitting methods for SDEs satisfying a commutativity condition
James Foster, Goncalo dos Reis, Calum Strange
In this paper, we introduce a new simple approach to developing and establishing the convergence of splitting methods for a large class of stochastic differential equations (SDEs),…
Efficient and Accurate Gradients for Neural SDEs
Patrick Kidger, James Foster, Xuechen Li +1
Neural SDEs combine many of the best qualities of both RNNs and SDEs: memory efficient training, high-capacity function approximation, and strong priors on model space. This makes…
Brownian bridge expansions for Lévy area approximations and particular values of the Riemann zeta function
James Foster, Karen Habermann
We study approximations for the Lévy area of Brownian motion which are based on the Fourier series expansion and a polynomial expansion of the associated Brownian bridge. Comparing…
Neural SDEs as Infinite-Dimensional GANs
Patrick Kidger, James Foster, Xuechen Li +2
Stochastic differential equations (SDEs) are a staple of mathematical modelling of temporal dynamics. However, a fundamental limitation has been that such models have typically bee…
The shifted ODE method for underdamped Langevin MCMC
James Foster, Terry Lyons, Harald Oberhauser
In this paper, we consider the underdamped Langevin diffusion (ULD) and propose a numerical approximation using its associated ordinary differential equation (ODE). When used as a…
Neural Rough Differential Equations for Long Time Series
James Morrill, Cristopher Salvi, Patrick Kidger +2
Neural controlled differential equations (CDEs) are the continuous-time analogue of recurrent neural networks, as Neural ODEs are to residual networks, and offer a memory-efficient…
Neural Controlled Differential Equations for Irregular Time Series
Patrick Kidger, James Morrill, James Foster +1
Neural ordinary differential equations are an attractive option for modelling temporal dynamics. However, a fundamental issue is that the solution to an ordinary differential equat…
An asymptotic radius of convergence for the Loewner equation and simulation of traces via splitting
James Foster, Terry Lyons, Vlad Margarint
In this paper, we shall study the convergence of Taylor approximations for the backward Loewner differential equation (driven by Brownian motion) near the origin. More concretely,…
An optimal polynomial approximation of Brownian motion
James Foster, Terry Lyons, Harald Oberhauser
In this paper, we will present a strong (or pathwise) approximation of standard Brownian motion by a class of orthogonal polynomials. The coefficients that are obtained from the ex…