A Complete Decomposition of Stochastic Differential Equations

TL;DR

This paper presents a comprehensive decomposition of stochastic differential equations into three distinct components, providing a new framework for understanding their structure and behavior.

Contribution

It introduces a novel decomposition method for SDEs into scalar, symmetric, and skew-symmetric components, enhancing analytical understanding.

Findings

Decomposition applies to any SDE with prescribed marginals.

Unique scalar field governs marginal evolution.

Framework aids in analyzing SDE dynamics.

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.