feat: finite dimensional distribution of Brownian motion#36472
Open
EtienneC30 wants to merge 42 commits intoleanprover-community:masterfrom
Open
feat: finite dimensional distribution of Brownian motion#36472EtienneC30 wants to merge 42 commits intoleanprover-community:masterfrom
EtienneC30 wants to merge 42 commits intoleanprover-community:masterfrom
Conversation
This reverts commit fd419e7.
EtienneC30
added
blocked-by-other-PR
PR summary 595196b114
|
| File | Base Count | Head Count | Change |
|---|---|---|---|
| Mathlib.MeasureTheory.Function.L2Space | 2372 | 2383 | +11 (+0.46%) |
| Mathlib.Probability.Moments.Basic | 2455 | 2466 | +11 (+0.45%) |
| Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic | 2731 | 2742 | +11 (+0.40%) |
Import changes for all files
| Files | Import difference |
|---|---|
5 filesMathlib.Probability.Distributions.Gaussian.CharFun Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Independence Mathlib.Probability.Distributions.Gaussian.IsGaussianProcess.Independence Mathlib.Probability.Distributions.Gaussian.Multivariate Mathlib.Probability.Moments.CovarianceBilin |
1 |
12 filesMathlib.NumberTheory.LSeries.DirichletContinuation Mathlib.NumberTheory.LSeries.Nonvanishing Mathlib.NumberTheory.LSeries.PrimesInAP Mathlib.NumberTheory.LSeries.ZMod Mathlib.NumberTheory.MahlerMeasure Mathlib.NumberTheory.ModularForms.DedekindEta Mathlib.NumberTheory.ModularForms.Delta Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.MDifferentiable Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Summable Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Transform Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion Mathlib.NumberTheory.ModularForms.JacobiTheta.Manifold |
9 |
98 filesMathlib.Analysis.Distribution.FourierMultiplier Mathlib.Analysis.Distribution.SchwartzSpace.Basic Mathlib.Analysis.Distribution.SchwartzSpace.Deriv Mathlib.Analysis.Distribution.SchwartzSpace.Fourier Mathlib.Analysis.Distribution.SchwartzSpace Mathlib.Analysis.Distribution.TemperedDistribution Mathlib.Analysis.Fourier.AddCircleMulti Mathlib.Analysis.Fourier.AddCircle Mathlib.Analysis.Fourier.Convolution Mathlib.Analysis.Fourier.FourierTransformDeriv Mathlib.Analysis.Fourier.LpSpace Mathlib.Analysis.Fourier.PoissonSummation Mathlib.Analysis.Polynomial.Fourier Mathlib.Analysis.Polynomial.MahlerMeasure Mathlib.Analysis.SpecialFunctions.Gaussian.PoissonSummation Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1 Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2 Mathlib.MeasureTheory.Function.ConditionalExpectation.Indicator Mathlib.MeasureTheory.Function.ConditionalExpectation.LebesgueBochner Mathlib.MeasureTheory.Function.ConditionalExpectation.PullOut Mathlib.MeasureTheory.Function.ConditionalExpectation.RadonNikodym Mathlib.MeasureTheory.Function.ConditionalExpectation.Real Mathlib.MeasureTheory.Function.ConditionalLExpectation Mathlib.MeasureTheory.Function.FactorsThrough Mathlib.MeasureTheory.Function.L2Space Mathlib.MeasureTheory.Measure.CharacteristicFunction.TaylorExpansion Mathlib.MeasureTheory.Measure.LevyConvergence Mathlib.NumberTheory.EulerProduct.DirichletLSeries Mathlib.NumberTheory.Harmonic.ZetaAsymp Mathlib.NumberTheory.LSeries.Dirichlet Mathlib.NumberTheory.LSeries.HurwitzZetaEven Mathlib.NumberTheory.LSeries.HurwitzZetaOdd Mathlib.NumberTheory.LSeries.HurwitzZetaValues Mathlib.NumberTheory.LSeries.HurwitzZeta Mathlib.NumberTheory.LSeries.RiemannZeta Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Defs Mathlib.NumberTheory.ModularForms.JacobiTheta.Bounds Mathlib.NumberTheory.ModularForms.JacobiTheta.OneVariable Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable Mathlib.NumberTheory.ZetaValues Mathlib.Probability.BorelCantelli Mathlib.Probability.Combinatorics.BinomialRandomGraph.Defs Mathlib.Probability.CondVar Mathlib.Probability.ConditionalExpectation Mathlib.Probability.Distributions.Gaussian.Basic Mathlib.Probability.Distributions.Gaussian.Fernique Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Def Mathlib.Probability.Distributions.Gaussian.IsGaussianProcess.Basic Mathlib.Probability.Distributions.Gaussian.IsGaussianProcess.Def Mathlib.Probability.Distributions.Gaussian.Real Mathlib.Probability.Distributions.SetBernoulli Mathlib.Probability.HasLawExists Mathlib.Probability.HasLaw Mathlib.Probability.IdentDistribIndep Mathlib.Probability.IdentDistrib Mathlib.Probability.Independence.BoundedContinuousFunction Mathlib.Probability.Independence.Conditional Mathlib.Probability.Independence.InfinitePi Mathlib.Probability.Independence.Integration Mathlib.Probability.Independence.ZeroOne Mathlib.Probability.Kernel.CompProdEqIff Mathlib.Probability.Kernel.Composition.AbsolutelyContinuous Mathlib.Probability.Kernel.CondDistrib Mathlib.Probability.Kernel.Condexp Mathlib.Probability.Kernel.Disintegration.Density Mathlib.Probability.Kernel.Disintegration.Integral Mathlib.Probability.Kernel.Disintegration.StandardBorel Mathlib.Probability.Kernel.Disintegration.Unique Mathlib.Probability.Kernel.IonescuTulcea.Traj Mathlib.Probability.Kernel.Posterior Mathlib.Probability.Kernel.RadonNikodym Mathlib.Probability.Martingale.Basic Mathlib.Probability.Martingale.BorelCantelli Mathlib.Probability.Martingale.Centering Mathlib.Probability.Martingale.Convergence Mathlib.Probability.Martingale.OptionalSampling Mathlib.Probability.Martingale.OptionalStopping Mathlib.Probability.Martingale.Upcrossing Mathlib.Probability.Moments.Basic Mathlib.Probability.Moments.ComplexMGF Mathlib.Probability.Moments.CovarianceBilinDual Mathlib.Probability.Moments.Covariance Mathlib.Probability.Moments.MGFAnalytic Mathlib.Probability.Moments.SubGaussian Mathlib.Probability.Moments.Tilted Mathlib.Probability.Moments.Variance Mathlib.Probability.Notation Mathlib.Probability.Process.Adapted Mathlib.Probability.Process.Filtration Mathlib.Probability.Process.FiniteDimensionalLaws Mathlib.Probability.Process.HittingTime Mathlib.Probability.Process.PartitionFiltration Mathlib.Probability.Process.Predictable Mathlib.Probability.Process.Stopping Mathlib.Probability.ProductMeasure Mathlib.Probability.StrongLaw |
11 |
Mathlib.Probability.BrownianMotion.GaussianProjectiveFamily (new file) |
2848 |
Declarations diff
+ HasGaussianLaw.map_eq_gaussianReal
+ _root_.MeasureTheory.posSemidef_matrix_measure_inter
+ brownianCovMatrix
+ brownianCovMatrix_apply
+ brownianCovMatrix_submatrix
+ covariance_eval_gaussianProjectiveFamily
+ covariance_gaussianProjectiveFamily
+ gaussianProjectiveFamily
+ integral_comp_id_comm
+ integral_comp_id_comm'
+ integral_eval_gaussianProjectiveFamily
+ integral_gaussianProjectiveFamily
+ integral_id_gaussianProjectiveFamily
+ integral_id_gaussianProjectiveFamily'
+ integral_id_map
+ isGaussian_gaussianProjectiveFamily
+ isProjectiveMeasureFamily_gaussianProjectiveFamily
+ measurePreserving_eval_gaussianProjectiveFamily
+ measurePreserving_eval_sub_eval_gaussianProjectiveFamily
+ measurePreserving_ofLp_multivariateGaussian
+ measurePreserving_restrict_gaussianProjectiveFamily
+ measurePreserving_toLp_gaussianProjectiveFamily
+ posSemidef_brownianCovMatrix
+ variance_eval_gaussianProjectiveFamily
+ variance_gaussianProjectiveFamily
You can run this locally as follows
## summary with just the declaration names:
./scripts/pr_summary/declarations_diff.sh <optional_commit>
## more verbose report:
./scripts/pr_summary/declarations_diff.sh long <optional_commit>The doc-module for scripts/pr_summary/declarations_diff.sh contains some details about this script.
Increase in tech debt: (relative, absolute) = (2.00, 0.00)
| Current number | Change | Type |
|---|---|---|
| 9490 | 2 | backward.isDefEq |
Current commit 99180b3cc5
Reference commit 595196b114
You can run this locally as
./scripts/reporting/technical-debt-metrics.sh pr_summary
- The
relativevalue is the weighted sum of the differences with weight given by the inverse of the current value of the statistic. - The
absolutevalue is therelativevalue divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).
2 tasks
EtienneC30
removed
the
blocked-by-other-PR
|
This PR/issue depends on:
|
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
2 participants
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
Define
gaussianProjectiveFamily : (I : Finset ℝ≥0) → Measure (I → ℝ). EachgaussianProjectiveFamily Iis the centered Gaussian measure overI → ℝwith covariance matrix given bybrownianCovMatrix I s t := min s t.Prove that these measures satisfy
IsProjectiveMeasureFamily, which means that they can be extended into a measure overℝ≥0 → ℝthanks to the Kolmogorov's extension theorem (not in Mathlib yet). The obtained measure is a measure over the set of real processes indexed byℝ≥0and is the law of the Brownian motion.