Status:
Personal website:
Research groups:
Address
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
Research interests:
Stochastic analysis, rough path theory, differential equations and machine learning.
I am particularly interested in numerical methods for SDEs. My DPhil thesis is on this topic and can be found here.
Some recent work on Brownian motion was 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: 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:
The shifted ODE method for underdamped Langevin MCMC
James Foster, Terry Lyons and Harald Oberhauser (2021)
arXiv:2101.03446
An optimal polynomial approximation of Brownian motion
James Foster, Terry Lyons and Harald Oberhauser,
SIAM Journal on Numerical Analysis (2020)
Neural SDEs Made Easy: SDEs are Infinite-Dimensional GANs
Patrick Kidger, James Foster, Xuechen Li, Harald Oberhauser and Terry Lyons,
Machine Learning and the Physical Sciences, NeurIPS workshop (2020)
Neural CDEs for Long Time Series via the Log-ODE Method
James Morrill, Patrick Kidger, Cristopher Salvi, James Foster and Terry Lyons,
Machine Learning and the Physical Sciences, NeurIPS workshop (2020)
Computing the untruncated signature kernel as the solution of a Goursat problem
Thomas Cass, James Foster, Terry Lyons, Cristopher Salvi and Weixin Yang (2020)
arXiv:2006.14794
Neural Controlled Differential Equations for Irregular Time Series
Patrick Kidger, James Morrill, James Foster and Terry Lyons,
Neural Information Processing Systems 2020 (Spotlight)
An asymptotic radius of convergence for the Loewner equation and simulation of SLE traces via splitting
James Foster, Terry Lyons and Vlad Margarint (2019)
arXiv:1912.06424