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Concept

Martingale (probability theory)

Related lectures (32)

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

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

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

Covers the proof and recap of the martingale convergence theorem, focusing on the conditions for the existence of a random variable.

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

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

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

Introduces the martingale convergence theorem and demonstrates its application with examples.

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

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

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

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

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

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

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

Covers the fundamental theorems of asset pricing, including EMM, self-financing strategies, risk-neutral pricing, and completeness of markets.

Explores martingale-based linear response, complex diffusivity, and Nyquist relation in stochastic systems with time-dependent perturbation.

Explores martingales, adaptability, and stopping times in stochastic processes.

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

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