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Add Brownian quadratic variation module - #487

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rohitmanokaran:codex/brownian-qv-cleanup
Draft

Add Brownian quadratic variation module#487
rohitmanokaran wants to merge 2 commits into
RemyDegenne:masterfrom
rohitmanokaran:codex/brownian-qv-cleanup

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@rohitmanokaran

@rohitmanokaran rohitmanokaran commented Jun 29, 2026

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Refs #432.

Summary

  • Add BrownianMotion.StochasticIntegral.QuadraticVariationBrownian and expose it from BrownianMotion.lean.
  • Use the post-feat: Use local square-integrability for quadratic variation #469 quadraticVariation API through the normalized Doob-Meyer predictable-part dependencies from the Advance Brownian quadratic variation #463 route.
  • Move the continuous-martingale local-square-integrability obligation to Martingale.isLocallySquareIntegrable_of_continuous, so the Brownian file depends on the general lemma instead of carrying Brownian-specific deterministic localization code.
  • Close quadraticVariation_brownian using the Brownian square-minus-time martingale decomposition and normalized predictable-part uniqueness.

Dependency notes

  • Rebased on upstream master through Blueprint update: classes of martingales #488.
  • QuadraticVariationBrownian.lean has no sorry.
  • Remaining placeholders are in dependency-layer APIs: continuous martingale implies locally square-integrable, and normalized Doob-Meyer existence/uniqueness.

Validation

  • lake build BrownianMotion.StochasticIntegral.QuadraticVariationBrownian
  • lake env lean BrownianMotion.lean


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).

@rohitmanokaran
rohitmanokaran marked this pull request as draft June 29, 2026 15:56
@rohitmanokaran rohitmanokaran changed the title [codex] add Brownian quadratic variation module Add Brownian quadratic variation module Jun 29, 2026
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