Our goal is to formalize Brownian motions in Lean using Mathlib. There are two main parts to this formalization:
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develop the theory of Gaussian distributions, build a projective family of Gaussian distributions and define its projective limit by the Kolmogorov extension theorem,
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prove the Kolmogorov-Chentsov continuity theorem.
Putting the two sides together, we can then build a stochastic process that fits the definition of a Brownian motion on the real line.
For more information, see the project home page, in particular the blueprint.
Zulip channel for discussion: zulip link
The project is ongoing and contributions are welcome.
Our github project uses the Leanblueprint tool by Patrick Massot and a lot of code from the LeanProject template by Pietro Monticone.