27 citations · 76 across the 9 of their papers we have counts for
10 papers
Simulating elliptic diffusions and orthogonal invariance
Charles Curry
We study numerical methods for simulating diffusions that exploit the orthogonal invariance of the Gaussian law, building on the work of Cruzeiro, Malliavin and Thalmeier.
Principal symmetric space analysis
Stephen R Marsland, Robert I McLachlan, Charles Curry
We develop a novel analogue of Euclidean PCA (principal component analysis) for data taking values on a Riemannian symmetric space, using totally geodesic submanifolds as approxima…
Convergence of Lie group integrators
Charles Curry, Alexander Schmeding
We relate two notions of local error for integration schemes on Riemannian homogeneous spaces, and show how to derive global error estimates from such local bounds. In doing so, we…
The Magnus expansion and Post-Lie algebras
Charles Curry, Kurusch Ebrahimi-Fard, Brynjulf Owren
We relate the classical and post-Lie Magnus expansions. Intertwining algebraic and geometric arguments allows to placing the classical Magnus expansion in the context of Lie group…
Planarly branched rough paths and rough differential equations on homogeneous spaces
Charles Curry, Kurusch Ebrahimi-Fard, Dominique Manchon +1
The central aim of this work is to understand rough differential equations on homogeneous spaces. We focus on the formal approach, by giving an explicit expansion of the solution a…
Quasi-shuffle algebras and renormalisation of rough differential equations
Yvain Bruned, Charles Curry, Kurusch Ebrahimi-Fard
The objective of this work is to compare several approaches to the process of renormalisation in the context of rough differential equations using the substitution bialgebra on roo…
Variable stepsize commutator free Lie group integrators
Charles Curry, Brynjulf Owren
We introduce variable stepsize commutator free Lie group integrators, where the error control is achieved using embedded Runge-Kutta pairs.
Algebraic Structures and Stochastic Differential Equations driven by Levy processes
Charles Curry, Kurusch Ebrahimi-Fard, Simon J. A. Malham +1
We construct an efficient integrator for stochastic differential systems driven by Levy processes. An efficient integrator is a strong approximation that is more accurate than the…
Rooted trees, non-rooted trees and hamiltonian B-series
Geir Bogfjellmo, Charles H. Curry, Dominique Manchon
We explore the relationship between (non-planar) rooted trees and free trees, i.e. without root. We give in particular, for non-rooted trees, a substitute for the Lie bracket given…
Levy Processes and Quasi-Shuffle Algebras
Charles Curry, Kurusch Ebrahimi-Fard, Simon J. A. Malham +1
We investigate the algebra of repeated integrals of semimartingales. We prove that a minimal family of semimartingales generates a quasi-shuffle algebra. In essence, to fulfill the…