Martingales and Brownian Motion

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Related lectures (35)

Martingale Convergence

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

Doob's Martingale

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

Martingale Convergence Theorem

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

Doob's Decomposition Theorem

Covers Doob's decomposition theorem for submartingales and explores Brownian motion properties, quadratic variation, and continuous martingales.

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.

Generalization of Martingales: Sub- & Supermartingales

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

Martingale Convergence Theorems

Explores the convergence of martingales under specific conditions and previews upcoming topics on martingale theorems and inequalities.

Martingale Convergence Theorem: Version 1

Introduces the martingale convergence theorem and demonstrates its application with examples.

Girsanov: Martingales and Brownian Motion

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

Stochastic Integration: First Steps

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

Stopping Times: Martingales and Brownian Motion

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

Generalizations to Sub- & Supermartingales

Covers the generalizations of sub- & supermartingales and the existence of random variables.

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.

Sub- and Supermartingales: Theory and Applications

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

Martingale Convergence Theorem

Explores the proof of the martingale convergence theorem and the conditions for convergence to a random variable.

Optional Stopping Theorem: Proof and Applications

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

Optional Stopping Theorem: Martingales and Stepping Times

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

Martingales and Brownian Motion Log in to Mediaspace to watch this video

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

Girsanov's Theorem: Numerical Simulation of SDEs Log in to Mediaspace to watch this video

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

Martingales and Brownian Motion Construction Log in to Mediaspace to watch this video

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

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