Lectures related to Martingales and Brownian Motion

Martingales and Brownian Motion: Construction and Properties

Explores the construction and properties of a Brownian motion with continuous trajectories using Paul Lévy's method.

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.

Partial Derivatives: Part 1

Explores partial derivatives, continuity of functions, mean value theorem, and uniform continuity.

Derivative of Integral with Parameter Dependency

Explores the derivative of an integral with parameter dependency and its continuity.

Continuous Functions: Definition

Explains the definition of continuous functions and isolated points.

Analysis II: Abstract Integration

Explores the extension of functions and the conditions for continuity.

Continuous Functions and Continuity Extension

Covers the concept of continuous functions and their extension to the closure of the domain.

Intermediate Value Theorem

Explores the Intermediate Value Theorem, continuous functions, and the verification of their continuity in various examples.

Martingales and Brownian Motion: Part 1

Explores transformations of Brownian motion, Markov properties, and scaling invariance.

Continuous Functions: Definitions and Continuity Criteria

Explains continuous functions, criteria for continuity, and continuity concepts at points and intervals.

Continuous Functions on Closed Interval

Explores continuous functions on closed intervals, emphasizing the importance of understanding definitions for continuity.

Demonstration of Uniqueness Theorem

Presents a detailed proof of the uniqueness theorem for functions f and g.