The strong convergence of operator-splitting methods for the Langevin dynamics model
Numerical Analysis
2020-08-11 v2 Numerical Analysis
Abstract
We study the strong convergence of some operator-splitting methods for the Langevin dynamics model with additive noise. It will be shown that a direct splitting of deterministic and random terms, including the symmetric splitting methods, only offers strong convergence of order 1. To improve the order of strong convergence, a new class of operator-splitting methods based on Kunita's solution representation are proposed. We present stochastic algorithms with strong orders up to 3. Both mathematical analysis and numerical evidence are provided to verify the desired order of accuracy.
Keywords
Cite
@article{arxiv.1706.04237,
title = {The strong convergence of operator-splitting methods for the Langevin dynamics model},
author = {Adam Telatovich and Xiantao Li},
journal= {arXiv preprint arXiv:1706.04237},
year = {2020}
}