Status:
Personal website:
+44 1865 280600
Research groups:
Address
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
Research interests:
Stochastic analysis, differential equations, machine learning and rough path theory
I am particularly interested in numerical methods for stochastic differential equations (which was the topic of my DPhil thesis).
The main result of my DPhil thesis provides an interesting connection between Brownian motion and random polynomials.
A poster illustrating this idea can be found here.
Some of this work was also demonstrated in the Matlab example:
https://www.chebfun.org/examples/stats/RandomPolynomials.html
(courtesy of Prof. Nick Trefethen)
Teaching:
Graduate lecturer at Worcester College, tutoring Linear Algebra and Analysis (2017-2018)
TT 2019: Tutor (Consultation Sessions) - B8.4 Information Theory
MT 2018, HT 2021: Tutor - B8.4 Information Theory
TT 2017, 2018: Tutor (Consultation Sessions) - B8.4 Communication Theory
MT 2016, 2017: Teaching Assistant - B8.4 Communication Theory
HT 2017: Teaching Assistant - B8.3 Mathematical Models of Financial Derivatives
Prizes, awards, and scholarships:
G-Research PhD Prize (2020, first place)
Major / recent publications:
Efficient and Accurate Gradients for Neural SDEs
Patrick Kidger, James Foster, Xuechen Li and Terry Lyons
arXiv:2105.13493
Neural SDEs as Infinite-Dimensional GANs
Patrick Kidger, James Foster, Xuechen Li, Harald Oberhauser and Terry Lyons
International Conference on Machine Learning 2021
Neural Rough Differentail Equations for Long Time Series
James Morrill, Cristopher Salvi, Patrick Kidger, James Foster and Terry Lyons
International Conference on Machine Learning 2021
Brownian bridge expansions for Lévy area approximations and particular values of the Riemann zeta function
James Foster and Karen Habermann
arXiv:2102.10095
The shifted ODE method for underdamped Langevin MCMC
James Foster, Terry Lyons and Harald Oberhauser
arXiv:2101.03446
The Signature Kernel is the solution of a Goursat PDE
Cristopher Salvi, Thomas Cass, James Foster, Terry Lyons and Weixin Yang
To appear in the SIAM Journal on Mathematics of Data Science
Neural Controlled Differential Equations for Irregular Time Series
Patrick Kidger, James Morrill, James Foster and Terry Lyons
Neural Information Processing Systems 2020 (Spotlight)
An optimal polynomial approximation of Brownian motion
James Foster, Terry Lyons and Harald Oberhauser
SIAM Journal on Numerical Analysis (2020)
An asymptotic radius of convergence for the Loewner equation and simulation of SLE traces via splitting
James Foster, Terry Lyons and Vlad Margarint
arXiv:1912.06424