Add Brownian quadratic variation module - #487
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RemyDegenne
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| The localizing sequence is given by deterministic positive horizons. -/ | ||
| lemma locally_isSquareIntegrable_brownian : | ||
| IsLocallySquareIntegrable brownian brownianNaturalFiltration gaussianLimit := by |
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You should prove the more general result that a continuous martingale is locally square integrable (in a new PR).
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Refs #432.
Summary
BrownianMotion.StochasticIntegral.QuadraticVariationBrownianand expose it fromBrownianMotion.lean.quadraticVariationAPI through the normalized Doob-Meyer predictable-part dependencies from the Advance Brownian quadratic variation #463 route.Martingale.isLocallySquareIntegrable_of_continuous, so the Brownian file depends on the general lemma instead of carrying Brownian-specific deterministic localization code.quadraticVariation_brownianusing the Brownian square-minus-time martingale decomposition and normalized predictable-part uniqueness.Dependency notes
masterthrough Blueprint update: classes of martingales #488.QuadraticVariationBrownian.leanhas nosorry.Validation
lake build BrownianMotion.StochasticIntegral.QuadraticVariationBrownianlake env lean BrownianMotion.lean