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Lecture
Martingales and Brownian Motion
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Martingales and Brownian Motion: Construction and Properties
Explores the construction and properties of a Brownian motion with continuous trajectories using Paul Lévy's method.
Doob's Decomposition Theorem
Covers Doob's decomposition theorem for submartingales and explores Brownian motion properties, quadratic variation, and continuous martingales.
Advanced Analysis 2: Continuity and Limits
Delves into advanced analysis topics, emphasizing continuity, limits, and uniform continuity.
Martingales and Brownian Motion: Drift and Exit Time
Explores Brownian motion with drift, exit probabilities, and average exit times from intervals.
Martingales and Brownian Motion
Discusses convergence, martingales, Brownian motion, joint laws, testing procedures, and stop times.
Levy Flights & Brownian Motion
Explores Levy Flights and Brownian Motion, focusing on probability distributions and divergences in lag time.
Existence of Solutions for Poisson-Dirichlet Problem
Covers the existence of solutions for the Poisson-Dirichlet problem, focusing on showing that certain conditions hold for locally bounded and Hölder continuous functions.
Martingales and Brownian Motion: Global Behavior and Zero Set Length
Explores the behavior of Brownian motion and its zero set length.
Martingales and Brownian Motion Construction
Explores the construction of Brownian motion with continuous trajectories and the dimension of its zero set.
Advanced Analysis II: Matrix Diagonalization
Covers matrix diagonalization, compact sets, continuity of functions, and the Mandelbrot set.
