Lectures related to Doob's Decomposition Theorem

Martingale Convergence Theorem: Proof and Recap

Covers the proof and recap of the martingale convergence theorem, focusing on the conditions for the existence of a random variable.

Martingale Convergence

Explores martingale convergence, discussing the conditions for convergence and variance in martingales.

Stochastic Integration: First Steps

Covers stochastic integration, process bracket, martingales, and variations in submartingales.

Stochastic Calculus: Brownian Motion

Explores stochastic processes in continuous time, emphasizing Brownian motion and related concepts.

Doob's Martingale

Covers the concept of Doob's martingale and its properties, including integrability and convergence theorem.

Stochastic Calculus: Integrals and Processes

Explores stochastic calculus, emphasizing integrals, processes, martingales, and Brownian motion.

Martingale Convergence Theorem

Covers the proof of the martingale convergence theorem and the convergence of the martingale sequence almost surely.

Stochastic Calculus: Itô's Formula

Covers Stochastic Calculus, focusing on Itô's Formula, Stochastic Differential Equations, martingale properties, and option pricing.

Girsanov's Theorem: Numerical Simulation of SDEs

Covers Girsanov's Theorem, absolutely continuous measures, and numerical simulation of Stochastic Differential Equations (SDEs) with applications in finance.

Quadratic Variation: Martingales and Stochastic Integrals

Explores quadratic variation in martingales and stochastic integrals, emphasizing their properties and extensions.

Girsanov: Martingales and Brownian Motion

Explores martingales, Brownian motion, and measure transformations in probability theory.

Martingale Convergence Theorem: Proof and Stopping Time

Explores the proof of the martingale convergence theorem and the concept of stopping time in square-integrable martingales.

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 Construction

Explores the construction of Brownian motion with continuous trajectories and the dimension of its zero set.

Joint Quadratic Processes

Covers the concept of joint quadratic processes and their properties.

Sub- and Supermartingales: Theory and Applications

Explores sub- and supermartingales, stopping times, and their applications in stochastic processes.

Martingales and Brownian Motion: Construction and Properties

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

Martingale Convergence Theorem

Explains the martingale convergence theorem and its applications in probability theory.

Martingales and Brownian Motion

Discusses convergence, martingales, Brownian motion, joint laws, testing procedures, and stop times.

Martingales and Brownian Motion

Explores the concept of martingales and their relation to Brownian motion through symmetric simple random walks and discusses the potential positive outcomes from the current crisis.