Martingales and Brownian Motion

Related lectures (32)

Page 3 of 4

Explores three stopping theorems in martingales and Brownian motion.

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

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

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

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

Explores the behavior of Brownian motion and its zero set length.

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

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

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

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