Modify the Improved Euler scheme to integrate stochastic differential equations
By Anthony J. Roberts. 2012
36 citations recorded by the source corpus.
A practical and new Runge–Kutta numerical scheme for stochastic differential equations is explored. Numerical examples demonstrate the strong convergence of the method. The first order strong conver
Subfields: Finance, Numerical Methods & Scientific Computing
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Finance
- Tim Dockhorn
- Alexia Jolicoeur-Martineau
- Remi Piche-Taillefer
- Ke Li
- Tal Kachman
- Ioannis Mitliagkas
- Karsten Kreis
- Arash Vahdat
In Numerical Methods & Scientific Computing
- Tim Dockhorn
- Alexia Jolicoeur-Martineau
- Timo Aila
- Remi Piche-Taillefer
- Miika Aittala
- Ke Li
- Tal Kachman
- Tero Karras
Citations in the corpus
- Elucidating the Design Space of Diffusion-Based Generative Models (2022, background): “The dots indicate lowest observed FID. higher-order adaptive SDE solver [40] and its performance is a good baseline for such solvers in general.”
- Gotta Go Fast When Generating Data with Score-Based Models (2021, methodology): “…2003] as in Lamba [2003] or a high-order stochastic Runge-Kutta method [Rößler, 2010] as in Rackauckas and Nie [2017b] (which did not work well in our preliminary attempts with the Julia package) we instead rely on the stochastic Improved Euler’s method [Roberts, 2012] as our higher order method.”
- Score-Based Generative Modeling with Critically-Damped Langevin Diffusion (2021, methodology): “GGF uses standard Euler-based methods under the hood (Kloeden & Platen, 1992; Roberts, 2012), in contrast to our SSCS that is derived from first principles.”