Lectures related to Local martingale

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

Girsanov: Martingales and Brownian Motion

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

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.

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.

Doob's Martingale

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

Optional Stopping Theorem: Proof and Applications

Covers the optional stopping theorem for martingales, providing a detailed proof and discussing its implications.

Joint Quadratic Processes

Covers the concept of joint quadratic processes and their properties.

Martingale Convergence Theorem

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

Martingale Convergence Theorem

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

Stochastic Integration: First Steps

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

Stochastic Integral: Isometry Continuity

Covers stochastic integrals, emphasizing isometry and continuity properties in martingales and different spaces.

Martingales and Stochastic Integration

Covers martingales, stochastic integration, and localizing processes using stopping times.

Stochastic Calculus: Itô's Formula

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

Stochastic Calculus: Integrals and Processes

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

Optional Stopping Theorem: Martingales and Stepping Times

Explores the optional stopping theorem for martingales and stepping times, emphasizing its applications and implications.

Stopping Times: Martingales and Brownian Motion

Explores stopping times in martingales and Brownian motion, discussing convergence properties and the strong Markov property.

Martingales and Brownian Motion: Drift and Exit Time

Explores Brownian motion with drift, exit probabilities, and average exit times from intervals.

Generalization of Martingales: Sub- & Supermartingales

Explores the generalization of martingales to sub- and supermartingales with a focus on convergence properties.

Martingales and Brownian Motion

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