3 papers
math.NA2025
On the convergence of adaptive approximations for stochastic differential equations
James Foster, Andraž JelinÄiÄ
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…
math.NA2025
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.NA2025
Single-seed generation of Brownian paths and integrals for adaptive and high order SDE solvers
Andraž JelinÄiÄ, 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…