Lectures related to Martingales: Definitions and Theorems

Martingales and Brownian Motion: Three Stopping Theorems

Explores three stopping theorems in martingales and Brownian motion.

Martingale Convergence

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

Reflection Principle: Proof and Observations

Covers the reflection principle and martingale writing in simple symmetric random walks.

Martingales and Stochastic Integration

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

Proofs: Logic, Mathematics & Algorithms

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Martingales: Definitions and Properties

Explores the definitions and properties of martingales in probability theory, including key concepts and examples.

Girsanov's Theorem: Numerical Simulation of SDEs

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

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Fundamental Groups

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.