feat: law of the iterated logarithm - #420
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RemyDegenne
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May 1, 2026
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Could you merge the master branch into yours and then run lake exe mk_all --module to add your new file to the imports of the BrownianMotion.lean file?
added 6 commits
May 3, 2026 12:52
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Thanks for the review @RemyDegenne! It's my first time proving a 'nontrivial' (for some definition of nontrivial) theorem in lean, so any feedback is much appreciated. |
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This PR adds a proof of the law of the iterated logarithm for Brownian motion, stating that
The statement is given by
IsBrownian.ae_limsup_div_sqrt_log_log_eq_one, and only uses the assumptionIsBrownian X P. The proof is the one from Kallenberg.There are however two
sorry-ful lemmas, namelyIsBrownian.reflectionandIsStandardGaussian.tail.The latter can be formalized right now, but the former relies on the strong Markov property for Brownian motion, which might benefit from being proved in higher generality (for example, for Feller processes).