Lecture

Stochastic Simulation: Theory of Markov Chains

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Explores Markov chain convergence, emphasizing invariant distribution, Law of Large Numbers, and mean rewards computation.

Explores the coupling of Markov chains and the proof of the ergodic theorem, emphasizing distribution convergence and chain properties.

Explores Markov chains and their applications in algorithms, focusing on user impatience and faithful sample generation.

Covers the theory and applications of Markov chains in modeling random phenomena and decision-making under uncertainty.

Explores probability convergence, discussing conditions for random variable sequences to converge and the uniqueness of convergence.

Covers Markov chains, coupled chains, and their applications, emphasizing the importance of irreducibility.

Explains the proof of the ergodic theorem and the concept of positive-recurrence in Markov chains.

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

Explores optimal transport in heat equations and metric spaces.

Covers Markov chains decomposition, LLN proof, Inventory Model application, and average costs.

Explores convergence in law for random variables, including Kolmogorov's theorem and proofs based on probability lemmas.

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

Explores stable laws, limit theorems, and random variable properties.

Explores the convergence of Fourier series in L² space with trigonometric polynomials and approximation theorems.

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Covers the introduction and properties of Markov chains, including transition matrices and stochastic processes.

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Explores Markov chains and algorithm applications, including exact simulation and Propp-Wilson algorithms.

Explores the composition of applications in mathematics and the importance of understanding their properties.