Optional Stopping Theorem: Martingales and Stepping Times

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

Explores three stopping theorems in martingales and Brownian motion.

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

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

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

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

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

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

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

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