A Complete Decomposition of Stochastic Differential Equations
Probability
2026-01-13 v1 Machine Learning
Statistics Theory
Statistics Theory
Abstract
We show that any stochastic differential equation with prescribed time-dependent marginal distributions admits a decomposition into three components: a unique scalar field governing marginal evolution, a symmetric positive-semidefinite diffusion matrix field and a skew-symmetric matrix field.
Keywords
Cite
@article{arxiv.2601.07834,
title = {A Complete Decomposition of Stochastic Differential Equations},
author = {Samuel Duffield},
journal= {arXiv preprint arXiv:2601.07834},
year = {2026}
}