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π Course Notes
π Course Notes
π Stochastic Differential Equations
π Stochastic Differential Equations
SDE Course Overview
π Notes
π Notes
Ch 1: Conditional Expectation
Ch 2: Brownian Motion
Ch 3: Stochastic Integrals
Ch 4: ItΓ΄ Integrals
Ch 5: Multivariate ItΓ΄ Calculus
Ch 6: Existence & Uniqueness
Ch 7: Option Pricing and Stopping Times
π Exercises
π Exercises
SDE Chapter 1-2
SDE Chapter 3-4
SDE Chapter 5-6
SDE Chapter 7
π Asymptotic Statistics
π Asymptotic Statistics
Asymptotic Statistics Course Overview
π Notes
π Notes
Ch 1: Stochastic Convergence
Ch 2: Characteristic Functions
Ch 3: Central Limit Theorem I
Ch 4: Central Limit Theorem II
Ch 5: Weakly Dependent Data I
Ch 6: Weakly Dependent Data II
Ch 7: Delta Method
Ch 8: Method of Moments
Ch 9: Maximum Likelihood Estimation I
Ch 10: Maximum Likelihood Estimation II
Ch 11: M-Estimation and Z-Estimation I
Ch 12: M-Estimation and Z-Estimation II
Ch 13: U-Statistics
Ch 14: Bootstrap
π Exercises
π Exercises
AS Homework 1
AS Homework 2
AS Homework 3
AS Homework 4
π Functional Analysis
π Functional Analysis
Functional Analysis Course Overview
π Notes
π Notes
Ch 1: Distance Spaces
Ch 2: Topology and Completeness
Ch 3: Compactness
Ch 4: Contraction Mapping Theorem
Ch 5: Normed Linear Spaces
Ch 6: Banach Spaces
Ch 7: Hilbert Spaces
Ch 8: Hilbert Space Theory
Ch 9: Linear Operators
Ch 10: Open Mapping and Closed Graph Theorems
Ch 11: Dual Spaces
Ch 12: Extension of Bounded Linear Functionals and Hahn-Banach Theorem
π© Point Set Topology
π© Point Set Topology
Point Set Topology Course Overview
π Notes
π Notes
Ch 1: Set Theory
Ch 2: Functions and Relations
Ch 3: Countable Sets
Ch 4: Open Sets and Topology
Ch 5: Induced Topology
Ch 6: Continuity and Homeomorphisms
Ch 7: Connectedness
Ch 8: Compactness
Ch 9: Compactness in Euclidean Spaces
Ch 10: Sequential Compactness
Ch 11: One-Point Compactification
Ch 12: Countability
Ch 13: Separation Axioms
π Exercises
π Exercises
Homework 1-2
Homework 3-4
Homework 5-6
Homework 7-9
𧱠Real Analysis
𧱠Real Analysis
Real Analysis Course Overview
π Notes
π Notes
Ch 1: Sigma-Algebras
Ch 2: Outer Measure
Ch 3: Lebesgue
Ch 4: Measurable Functions I
Ch 5: Measurable Functions II
Ch 6: Construction of the Integral
Ch 7: Convergence Theorems
Ch 8: Fubini's Theorem
Ch 9: Hahn-Jordan Decomposition
Ch 10: Radon-Nikodym Theorem
Ch 11: Fundamental Theorem of Calculus
Ch 12: L^p Spaces
π― Advanced Probability Theory
π― Advanced Probability Theory
Advanced Probability Theory Course Overview
π Notes
π Notes
Ch 1: Probability Spaces and Random Variables
Ch 2: Numerical Characteristics
Ch 3: Limit Theorems
β³ Advanced Mathematical Statistics
β³ Advanced Mathematical Statistics
Advanced Mathematical Statistics Course Overview
π Notes
π Notes
Ch 1: Gaussian Geometry and Classical Distributions
Ch 2: Sufficiency and Exponential Families
Ch 3: Completeness and UMVU
Ch 4: U-Statistics and Information Lower Bounds
Ch 5: Admissibility
Ch 6: Bayes' Rule
π Exercises
π Exercises
Homework 1
π² Matrix Computation
π² Matrix Computation
Matrix Computation Course Overview
π Notes
π Notes
Ch 1: Matrix Norms
Ch 2: Singular Value Decomposition
Ch 3: Gaussian Elimination and LU Decomposition
π€ Statistical Learning
π€ Statistical Learning
Statistical Learning Course Overview
π Notes
π Notes
Ch 1: K-Nearest Neighbors
Ch 2: Linear Regression
Ch 3: Penalized Linear Regression I
Ch 4: Penalized Linear Regression II
Ch 5: Classification Problems
Ch 6: Support Vector Machines
Ch 7: RKHS and Kernel Regression
Ch 8: Kernel Density Estimation
Ch 9: Tree Models
Ch 10: Causal Inference
π οΈ Quick Reference
π οΈ Quick Reference
π Overview
π οΈ Quick Reference
π οΈ Quick Reference
π Mathematical Statistics
π² Probability Theory
π Measure Theory
π’ Linear Algebra
π Stochastic Processes
π― Convex Optimization
π Regression Analysis
βΎοΈ Mathematical Analysis
π°οΈ Research Updates
π°οΈ Research Updates
π Latest Papers
ποΈ Lectures & Talks
ποΈ Lectures & Talks
π Overview
ποΈ Fundamental Theory
ποΈ Fundamental Theory
2025 Fall Advanced Probability Seminar
2025 Fall Advanced Probability Seminar
Large Deviation Principle (LDP)
π Paper Discussions
π Paper Discussions
2025 Fall Group Meetings
2025 Fall Group Meetings
Derandomized Knockoffs
Advanced Probability Theory Course Overview
π¬ Comments
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