Generalization of Martingales: Sub- & Supermartingales

About
Privacy
Disclaimer

Graph Chatbot

Related lectures (31)

Page 1 of 4

Doob's Martingale

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

Generalizations to Sub- & Supermartingales

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

Martingales and Brownian Motion: Convergence Criteria and Theorems

Explores convergence criteria for martingales, including almost sure convergence and Cauchy criterion, leading to the first martingale convergence theorem.

Martingale Convergence Theorem

Explores the proof of the martingale convergence theorem and the conditions for convergence to a random variable.

Martingale Convergence Theorem

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

Martingale Convergence Theorem: Proof and Recap

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

Stochastic Processes: Symmetric Random Walk

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

Optional Stopping Theorem

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

Central Limit Theorem

Covers the Central Limit Theorem and its application to random variables, proving convergence to a normal distribution.

Martingale Convergence Theorem: Version 1

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