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, 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, 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:
Brownian bridge expansions for Lévy area approximations and particular values of the Riemann zeta function
James Foster and Karen Habermann
arXiv:2102.10095
Neural SDEs as Infinite-Dimensional GANs
Patrick Kidger, James Foster, Xuechen Li, Harald Oberhauser and Terry Lyons
arXiv:2102.03657
The shifted ODE method for underdamped Langevin MCMC
James Foster, Terry Lyons and Harald Oberhauser
arXiv:2101.03446
An optimal polynomial approximation of Brownian motion
James Foster, Terry Lyons and Harald Oberhauser
SIAM Journal on Numerical Analysis (2020)
Neural Rough Differentail Equations for Long Time Series
James Morrill, Cristopher Salvi, Patrick Kidger, James Foster and Terry Lyons
arXiv:2009.08295
The Signature Kernel is the solution of a Goursat PDE
Cristopher Salvi, Thomas Cass, James Foster, Terry Lyons and Weixin Yang
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
arXiv:1912.06424