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444 stated across 47 posts

Every definition, theorem, and lemma across the writing, indexed by kind and linked to where it is stated.

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definitions57

definition 1The Mean-Variance Portfolio
definition 1Residues and Contour Integration
definition 1Holomorphic Functions and Cauchy's Theorem
definition 1Positive Definite Matrices
definition 1Eigenvalues and the Spectral Theorem
definition 1Convex Duality and the KKT Conditions
definition 1Convex Sets and Functions
definition 1Uniform Integrability and the Vitali Theorem
definition 1The L-p Spaces
definition 1Stochastic Differential Equations
definition 1Quadratic Variation
definition 5Quadratic Variation
definition 1Series and Power Series
definition 8Series and Power Series
definition 1The Riemann Integral
definition 1Differentiation and Taylor's Theorem
definition 1Price Formation in the Order Book
definition 10Price Formation in the Order Book
definition 1The Ornstein-Uhlenbeck Process
definition 1Martingales
definition 1Predictable Processes and Stopping Times
definition 3Predictable Processes and Stopping Times
definition 1Second-Order Processes and Mean-Square Calculus
definition 1Convergence and Limit Theorems
definition 1Gaussian Vectors and Processes
definition 3Gaussian Vectors and Processes
definition 7Gaussian Vectors and Processes
definition 1Characteristic Functions
definition 1Conditional Expectation
definition 1Independence
definition 1The Radon-Nikodym Theorem
definition 1Measures and Integration
definition 1Probability Spaces and Random Variables
definition 2Probability Spaces and Random Variables
definition 4Probability Spaces and Random Variables
definition 6Probability Spaces and Random Variables
definition 1Mercer's Theorem and Reproducing Kernels
definition 6Mercer's Theorem and Reproducing Kernels
definition 1Statistical Arbitrage
definition 4Statistical Arbitrage
definition 1Compact Operators and the Spectral Theorem
definition 5Compact Operators and the Spectral Theorem
definition 1Bounded Operators and the Adjoint
definition 4Bounded Operators and the Adjoint
definition 1Product Measures and Fubini's Theorem
definition 1Inner Product Spaces
definition 8Inner Product Spaces
definition 1Sigma-Algebras and Measures
definition 2Sigma-Algebras and Measures
definition 1Metric and Normed Spaces
definition 6Metric and Normed Spaces
definition 1Continuity and Limits of Functions
definition 3Continuity and Limits of Functions
definition 6Continuity and Limits of Functions
definition 1Sequences and Completeness
definition 2Sequences and Completeness
definition 6Sequences and Completeness

theorems114

theorem 1The Black-Scholes Equation
theorem 2The Black-Scholes Equation
theorem 3The Black-Scholes Equation
theorem 2The Mean-Variance Portfolio
theorem 3Residues and Contour Integration
theorem 5Residues and Contour Integration
theorem 3Holomorphic Functions and Cauchy's Theorem
theorem 4Holomorphic Functions and Cauchy's Theorem
theorem 5Holomorphic Functions and Cauchy's Theorem
theorem 2Positive Definite Matrices
theorem 3Positive Definite Matrices
theorem 3Eigenvalues and the Spectral Theorem
theorem 4Eigenvalues and the Spectral Theorem
theorem 2Convex Duality and the KKT Conditions
theorem 3Convex Duality and the KKT Conditions
theorem 4Convex Duality and the KKT Conditions
theorem 3Convex Sets and Functions
theorem 4Convex Sets and Functions
theorem 5Convex Sets and Functions
theorem 3Uniform Integrability and the Vitali Theorem
theorem 3The L-p Spaces
theorem 4The L-p Spaces
theorem 5The L-p Spaces
theorem 3Stochastic Differential Equations
theorem 4Stochastic Differential Equations
theorem 1Ito's Formula
theorem 2Ito's Formula
theorem 2Quadratic Variation
theorem 3Series and Power Series
theorem 4Series and Power Series
theorem 6Series and Power Series
theorem 2The Riemann Integral
theorem 3The Riemann Integral
theorem 4The Riemann Integral
theorem 5The Riemann Integral
theorem 4Differentiation and Taylor's Theorem
theorem 5Differentiation and Taylor's Theorem
theorem 6Differentiation and Taylor's Theorem
theorem 2The Karhunen-Loeve Expansion
theorem 3The Karhunen-Loeve Expansion
theorem 4The Karhunen-Loeve Expansion
theorem 2Price Formation in the Order Book
theorem 3Price Formation in the Order Book
theorem 5Price Formation in the Order Book
theorem 9Price Formation in the Order Book
theorem 11Price Formation in the Order Book
theorem 13Price Formation in the Order Book
theorem 14Price Formation in the Order Book
theorem 15Price Formation in the Order Book
theorem 2Change of Measure and Girsanov's Theorem
theorem 3Change of Measure and Girsanov's Theorem
theorem 2The Stochastic Integral
theorem 3The Stochastic Integral
theorem 1The Construction of Brownian Motion
theorem 2Martingales
theorem 3Martingales
theorem 4Martingales
theorem 5Martingales
theorem 2Second-Order Processes and Mean-Square Calculus
theorem 3Second-Order Processes and Mean-Square Calculus
theorem 4Second-Order Processes and Mean-Square Calculus
theorem 4Convergence and Limit Theorems
theorem 5Convergence and Limit Theorems
theorem 4Gaussian Vectors and Processes
theorem 8Gaussian Vectors and Processes
theorem 4Characteristic Functions
theorem 7Characteristic Functions
theorem 2Conditional Expectation
theorem 5Conditional Expectation
theorem 3Independence
theorem 4Independence
theorem 5Independence
theorem 6Independence
theorem 7Independence
theorem 2The Radon-Nikodym Theorem
theorem 4The Radon-Nikodym Theorem
theorem 2Measures and Integration
theorem 3Measures and Integration
theorem 5Measures and Integration
theorem 7Measures and Integration
theorem 7Probability Spaces and Random Variables
theorem 8Probability Spaces and Random Variables
theorem 10Probability Spaces and Random Variables
theorem 4Mercer's Theorem and Reproducing Kernels
theorem 3Statistical Arbitrage
theorem 4Compact Operators and the Spectral Theorem
theorem 3Bounded Operators and the Adjoint
theorem 5Bounded Operators and the Adjoint
theorem 3Orthonormal Bases
theorem 4Orthonormal Bases
theorem 5Orthonormal Bases
theorem 4Product Measures and Fubini's Theorem
theorem 5Product Measures and Fubini's Theorem
theorem 6Product Measures and Fubini's Theorem
theorem 1Projection and Riesz Representation
theorem 2Projection and Riesz Representation
theorem 4Projection and Riesz Representation
theorem 2L-squared and Completeness
theorem 2Inner Product Spaces
theorem 5Inner Product Spaces
theorem 7Inner Product Spaces
theorem 5Sigma-Algebras and Measures
theorem 3Metric and Normed Spaces
theorem 4Metric and Normed Spaces
theorem 5Metric and Normed Spaces
theorem 7Metric and Normed Spaces
theorem 2Continuity and Limits of Functions
theorem 4Continuity and Limits of Functions
theorem 5Continuity and Limits of Functions
theorem 7Continuity and Limits of Functions
theorem 3Sequences and Completeness
theorem 4Sequences and Completeness
theorem 5Sequences and Completeness
theorem 7Sequences and Completeness

propositions53

proposition 4The Mean-Variance Portfolio
proposition 4Residues and Contour Integration
proposition 2Holomorphic Functions and Cauchy's Theorem
proposition 4Positive Definite Matrices
proposition 2Eigenvalues and the Spectral Theorem
proposition 2Convex Sets and Functions
proposition 2Uniform Integrability and the Vitali Theorem
proposition 2Series and Power Series
proposition 9Series and Power Series
proposition 2Differentiation and Taylor's Theorem
proposition 3Differentiation and Taylor's Theorem
proposition 1The Karhunen-Loeve Expansion
proposition 5The Karhunen-Loeve Expansion
proposition 4Price Formation in the Order Book
proposition 6Price Formation in the Order Book
proposition 8Price Formation in the Order Book
proposition 12Price Formation in the Order Book
proposition 16Price Formation in the Order Book
proposition 2The Ornstein-Uhlenbeck Process
proposition 3The Ornstein-Uhlenbeck Process
proposition 4The Ornstein-Uhlenbeck Process
proposition 1Change of Measure and Girsanov's Theorem
proposition 1The Stochastic Integral
proposition 2Predictable Processes and Stopping Times
proposition 4Predictable Processes and Stopping Times
proposition 5Second-Order Processes and Mean-Square Calculus
proposition 2Convergence and Limit Theorems
proposition 2Gaussian Vectors and Processes
proposition 6Gaussian Vectors and Processes
proposition 2Characteristic Functions
proposition 3Characteristic Functions
proposition 3Conditional Expectation
proposition 4Conditional Expectation
proposition 3The Radon-Nikodym Theorem
proposition 6Measures and Integration
proposition 3Probability Spaces and Random Variables
proposition 5Probability Spaces and Random Variables
proposition 2Mercer's Theorem and Reproducing Kernels
proposition 7Mercer's Theorem and Reproducing Kernels
proposition 5Statistical Arbitrage
proposition 6Statistical Arbitrage
proposition 2Compact Operators and the Spectral Theorem
proposition 2Bounded Operators and the Adjoint
proposition 1Orthonormal Bases
proposition 2Product Measures and Fubini's Theorem
proposition 1L-squared and Completeness
proposition 3Inner Product Spaces
proposition 4Inner Product Spaces
proposition 6Inner Product Spaces
proposition 3Sigma-Algebras and Measures
proposition 4Sigma-Algebras and Measures
proposition 6Sigma-Algebras and Measures
proposition 2Metric and Normed Spaces

lemmas13

lemma 2Residues and Contour Integration
lemma 2The L-p Spaces
lemma 2Stochastic Differential Equations
lemma 5Series and Power Series
lemma 7Price Formation in the Order Book
lemma 3Convergence and Limit Theorems
lemma 6Characteristic Functions
lemma 2Independence
lemma 3Mercer's Theorem and Reproducing Kernels
lemma 2Statistical Arbitrage
lemma 3Compact Operators and the Spectral Theorem
lemma 2Orthonormal Bases
lemma 3Product Measures and Fubini's Theorem

corollaries16

corollary 3The Mean-Variance Portfolio
corollary 3Ito's Formula
corollary 4Ito's Formula
corollary 3Quadratic Variation
corollary 4Quadratic Variation
corollary 7Series and Power Series
corollary 4The Stochastic Integral
corollary 2The Construction of Brownian Motion
corollary 5Gaussian Vectors and Processes
corollary 5Characteristic Functions
corollary 4Measures and Integration
corollary 9Probability Spaces and Random Variables
corollary 5Mercer's Theorem and Reproducing Kernels
corollary 6Compact Operators and the Spectral Theorem
corollary 3Projection and Riesz Representation
corollary 3L-squared and Completeness

remarks2

remark Predictable Processes and Stopping Times
remark Statistical Arbitrage

proofs189

proof The Black-Scholes Equation
proof The Black-Scholes Equation
proof The Black-Scholes Equation
proof The Mean-Variance Portfolio
proof The Mean-Variance Portfolio
proof The Mean-Variance Portfolio
proof Residues and Contour Integration
proof Residues and Contour Integration
proof Residues and Contour Integration
proof Residues and Contour Integration
proof Holomorphic Functions and Cauchy's Theorem
proof Holomorphic Functions and Cauchy's Theorem
proof Holomorphic Functions and Cauchy's Theorem
proof Holomorphic Functions and Cauchy's Theorem
proof Positive Definite Matrices
proof Positive Definite Matrices
proof Positive Definite Matrices
proof Eigenvalues and the Spectral Theorem
proof Eigenvalues and the Spectral Theorem
proof Eigenvalues and the Spectral Theorem
proof Convex Duality and the KKT Conditions
proof Convex Duality and the KKT Conditions
proof Convex Duality and the KKT Conditions
proof Convex Sets and Functions
proof Convex Sets and Functions
proof Convex Sets and Functions
proof Convex Sets and Functions
proof Uniform Integrability and the Vitali Theorem
proof Uniform Integrability and the Vitali Theorem
proof The L-p Spaces
proof The L-p Spaces
proof The L-p Spaces
proof The L-p Spaces
proof Stochastic Differential Equations
proof Stochastic Differential Equations
proof Stochastic Differential Equations
proof Ito's Formula
proof Ito's Formula
proof Ito's Formula
proof Ito's Formula
proof Quadratic Variation
proof Quadratic Variation
proof Quadratic Variation
proof Series and Power Series
proof Series and Power Series
proof Series and Power Series
proof Series and Power Series
proof Series and Power Series
proof Series and Power Series
proof Series and Power Series
proof The Riemann Integral
proof The Riemann Integral
proof The Riemann Integral
proof The Riemann Integral
proof Differentiation and Taylor's Theorem
proof Differentiation and Taylor's Theorem
proof Differentiation and Taylor's Theorem
proof Differentiation and Taylor's Theorem
proof Differentiation and Taylor's Theorem
proof The Karhunen-Loeve Expansion
proof The Karhunen-Loeve Expansion
proof The Karhunen-Loeve Expansion
proof The Karhunen-Loeve Expansion
proof Price Formation in the Order Book
proof Price Formation in the Order Book
proof Price Formation in the Order Book
proof Price Formation in the Order Book
proof Price Formation in the Order Book
proof Price Formation in the Order Book
proof Price Formation in the Order Book
proof Price Formation in the Order Book
proof Price Formation in the Order Book
proof Price Formation in the Order Book
proof Price Formation in the Order Book
proof Price Formation in the Order Book
proof Price Formation in the Order Book
proof Price Formation in the Order Book
proof The Ornstein-Uhlenbeck Process
proof The Ornstein-Uhlenbeck Process
proof The Ornstein-Uhlenbeck Process
proof Change of Measure and Girsanov's Theorem
proof Change of Measure and Girsanov's Theorem
proof Change of Measure and Girsanov's Theorem
proof The Stochastic Integral
proof The Stochastic Integral
proof The Stochastic Integral
proof The Construction of Brownian Motion
proof The Construction of Brownian Motion
proof Martingales
proof Martingales
proof Martingales
proof Predictable Processes and Stopping Times
proof Predictable Processes and Stopping Times
proof Second-Order Processes and Mean-Square Calculus
proof Second-Order Processes and Mean-Square Calculus
proof Second-Order Processes and Mean-Square Calculus
proof Second-Order Processes and Mean-Square Calculus
proof Convergence and Limit Theorems
proof Convergence and Limit Theorems
proof Convergence and Limit Theorems
proof Convergence and Limit Theorems
proof Gaussian Vectors and Processes
proof Gaussian Vectors and Processes
proof Gaussian Vectors and Processes
proof Gaussian Vectors and Processes
proof Gaussian Vectors and Processes
proof Characteristic Functions
proof Characteristic Functions
proof Characteristic Functions
proof Characteristic Functions
proof Characteristic Functions
proof Characteristic Functions
proof Conditional Expectation
proof Conditional Expectation
proof Conditional Expectation
proof Conditional Expectation
proof Independence
proof Independence
proof Independence
proof Independence
proof Independence
proof Independence
proof The Radon-Nikodym Theorem
proof The Radon-Nikodym Theorem
proof Measures and Integration
proof Measures and Integration
proof Measures and Integration
proof Measures and Integration
proof Probability Spaces and Random Variables
proof Probability Spaces and Random Variables
proof Probability Spaces and Random Variables
proof Probability Spaces and Random Variables
proof Probability Spaces and Random Variables
proof Probability Spaces and Random Variables
proof Mercer's Theorem and Reproducing Kernels
proof Mercer's Theorem and Reproducing Kernels
proof Mercer's Theorem and Reproducing Kernels
proof Mercer's Theorem and Reproducing Kernels
proof Mercer's Theorem and Reproducing Kernels
proof Statistical Arbitrage
proof Statistical Arbitrage
proof Statistical Arbitrage
proof Statistical Arbitrage
proof Compact Operators and the Spectral Theorem
proof Compact Operators and the Spectral Theorem
proof Compact Operators and the Spectral Theorem
proof Compact Operators and the Spectral Theorem
proof Bounded Operators and the Adjoint
proof Bounded Operators and the Adjoint
proof Bounded Operators and the Adjoint
proof Orthonormal Bases
proof Orthonormal Bases
proof Orthonormal Bases
proof Orthonormal Bases
proof Orthonormal Bases
proof Product Measures and Fubini's Theorem
proof Product Measures and Fubini's Theorem
proof Product Measures and Fubini's Theorem
proof Product Measures and Fubini's Theorem
proof Product Measures and Fubini's Theorem
proof Projection and Riesz Representation
proof Projection and Riesz Representation
proof Projection and Riesz Representation
proof Projection and Riesz Representation
proof L-squared and Completeness
proof L-squared and Completeness
proof Inner Product Spaces
proof Inner Product Spaces
proof Inner Product Spaces
proof Inner Product Spaces
proof Inner Product Spaces
proof Inner Product Spaces
proof Sigma-Algebras and Measures
proof Sigma-Algebras and Measures
proof Sigma-Algebras and Measures
proof Sigma-Algebras and Measures
proof Metric and Normed Spaces
proof Metric and Normed Spaces
proof Metric and Normed Spaces
proof Metric and Normed Spaces
proof Metric and Normed Spaces
proof Continuity and Limits of Functions
proof Continuity and Limits of Functions
proof Continuity and Limits of Functions
proof Continuity and Limits of Functions
proof Sequences and Completeness
proof Sequences and Completeness
proof Sequences and Completeness
proof Sequences and Completeness