Law of large numbers

Formal sciences
Statistics
Statistical inference
Mathematical statistics

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Central Limit Theorem: Empirical Mean

Explores the convergence of empirical mean distributions towards Gaussian distributions, focusing on the Central Limit Theorem.

Markov Chains: Convergence and Equilibrium

Explores the convergence properties of Markov chains and the computation of long-run mean rewards.

Law of Large Numbers: General Assumptions

Delves into the complexities of extending from finite variance to finite expectation assumptions.

Law of Large Numbers: Strong Convergence

Explores the strong convergence of random variables and the normal distribution approximation in probability and statistics.

The Law of Large Numbers: Proof and Applications

Explores the proof and applications of the law of large numbers, emphasizing convergence of the empirical distribution.

Central Limit Theorem

Explores the Central Limit Theorem, convergence in law, characteristic functions, and moment problems in probability theory.

All of Probability: LLN, CLT, Chernoff and PAC bound

Covers the Law of Large Numbers, Central Limit Theorem, Chernoff bounds, and PAC bounds in probability theory.

Stochastic Processes: Symmetric Random Walk

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

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.

All of Probability: Basic Bounds, LLN & CLT

Introduces basic bounds, LLN, and CLT in probability theory, emphasizing convergence to normal distribution.