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arXiv · 2601.07834

A Complete Decomposition of Stochastic Differential Equations

Samuel Duffield
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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.

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Samuel Duffield. 2026-01-12. A Complete Decomposition of Stochastic Differential Equations. https://arxiv.org/abs/2601.07834

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