Sub- and Supermartingales: Theory and Applications

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Covers Stochastic Differential Equations, Wiener increment, Ito's lemma, and white noise integration in financial modeling.

Martingale-based Methods for Stochastic Systems

Explores martingales in stochastic systems, focusing on formal analysis, termination analysis, and stability verification.

Stochastic Calculus: Itô's Formula Log in to Mediaspace to watch this video

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

Stochastic Calculus: Brownian Motion Log in to Mediaspace to watch this video

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

Stochastic Calculus: Integrals and Processes Log in to Mediaspace to watch this video

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

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.

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

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

Stochastic Calculus: Lecture 1 Log in to Mediaspace to watch this video

Covers the essentials of probability, algebras, and conditional probability, including the Borel o-algebra and Poisson processes.

Stochastic Processes: Symmetric Random Walk Log in to Mediaspace to watch this video

Covers the properties of the symmetric random walk in stochastic processes.

Martingales and Brownian Motion: Drift and Exit Time Log in to Mediaspace to watch this video

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

Martingales and Brownian Motion: Three Stopping Theorems Log in to Mediaspace to watch this video

Explores three stopping theorems in martingales and Brownian motion.

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