A Short Proof of Strassen's Theorem Using Convex Analysis

TL;DR

This paper presents a straightforward proof of Strassen's theorem on stochastic dominance leveraging linear programming duality, avoiding measure-theoretic complexity, and extends the result to generalized inequalities via conic optimization.

Contribution

It offers a simplified, measure-theory-free proof of Strassen's theorem and introduces an intuitive optimization formulation for stochastic dominance, extending to conic inequalities.

Findings

Proof using linear programming duality simplifies understanding.

Extension to generalized inequalities via conic optimization.

Provides an alternative, intuitive formulation for stochastic dominance.

Abstract

We give a simple proof of Strassen's theorem on stochastic dominance using linear programming duality, without requiring measure-theoretic arguments. The result extends to generalized inequalities using conic optimization duality and provides an additional, intuitive optimization formulation for stochastic dominance.