3 papers
math.NA2024
Approximating the signature of Brownian motion for high order SDE simulation
James Foster
The signature is a collection of iterated integrals describing the "shape" of a path. It appears naturally in the Taylor expansions of controlled differential equations and, as a c…
math.NA2024
Single-seed generation of Brownian paths and integrals for adaptive and high order SDE solvers
Andraž Jelinčič, James Foster, Patrick Kidger
Despite the success of adaptive time-stepping in ODE simulation, it has so far seen few applications for Stochastic Differential Equations (SDEs). To simulate SDEs adaptively, meth…
math.NA2023
On the convergence of adaptive approximations for stochastic differential equations
James Foster, Andraž Jelinčič
In this paper, we study numerical approximations for stochastic differential equations (SDEs) that use adaptive step sizes. In particular, we consider a general setting where decis…