Martingale Convergence Theorem

Related lectures (31)

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

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

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

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

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

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

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

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

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

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