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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}
}
R2 v1 2026-07-01T09:01:17.685Z