Lectures related to Martingales: Definitions and Theorems

Optional Stopping Theorem: Proof and Applications

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

Sub- and Supermartingales: Theory and Applications

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

Stopping Times: Martingales and Brownian Motion

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

Doob's Martingale

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

Optional Stopping Theorem

Explores stopping times, the optional stopping theorem, F-measurable random variables, and martingales.

Martingale Convergence Theorem

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

Martingale Convergence Theorem

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

Optional Stopping Theorem: Martingales and Stepping Times

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

Martingale Convergence Theorem: Proof and Stopping Time

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

Generalization of Martingales: Sub- & Supermartingales

Explores the generalization of martingales to sub- and supermartingales with a focus on convergence properties.

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.