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arXiv · 2511.20118

Formalization of Brownian motion in Lean

Rémy Degenne·David Ledvinka·Etienne Marion·Peter Pfaffelhuber
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Abstract

Brownian motion is a building block in modern probability theory. In this paper, we describe a formalization of Brownian motion using the Lean theorem prover. We build on the existing measure-theoretic foundations in Lean's mathematical library, Mathlib, and we develop several key components needed for the construction of Brownian motion, including the Carath\'eodory and Kolmogorov extension theorems, Gaussian measures in Banach spaces, and the Kolmogorov-Chentsov theorem for path continuity.

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Rémy Degenne, David Ledvinka, Etienne Marion, Peter Pfaffelhuber. 2025-11-25. Formalization of Brownian motion in Lean. https://arxiv.org/abs/2511.20118

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