Martingale Convergence

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Advanced Probability: Summary

Covers random variables, sample spaces, probability distributions, functions, expected value, variance, and estimations.

Generalization of Martingales: Sub- & Supermartingales

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

Stochastic Processes: Review and Properties

Covers the review of random variables, probability density functions, variance, and Gaussian processes.

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.

Probabilities and Statistics: Key Theorems and Applications

Discusses key statistical concepts, including sampling dangers, inequalities, and the Central Limit Theorem, with practical examples and applications.

Advanced Probabilities: Random Variables & Expected Values

Explores advanced probabilities, random variables, and expected values, with practical examples and quizzes to reinforce learning.

Doob's Decomposition Theorem

Covers Doob's decomposition theorem for submartingales and explores Brownian motion properties, quadratic variation, and continuous martingales.

Independence and Covariance

Explores independence and covariance between random variables, discussing their implications and calculation methods.

Random Variables and Expected Value

Introduces random variables, probability distributions, and expected values through practical examples.

Generalizations to Sub- & Supermartingales

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