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Lecture
Continuous-Time Markov Chains: Reversible Chains
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Markov Chains and Algorithm Applications
Covers Markov chains and their applications in algorithms, focusing on Markov Chain Monte Carlo sampling and the Metropolis-Hastings algorithm.
Limiting Distribution and Ergodic Theorem
Explores limiting distribution in Markov chains and the implications of ergodicity and aperiodicity on stationary distributions.
Markov Chains: PageRank Algorithm
Explores the PageRank algorithm within Markov chains, emphasizing ergodicity and convergence for web page ranking.
Stochastic Processes: Time Reversal
Explores time reversal in stationary Markov chains and the concept of detailed balance conditions.
Ergodic Theorem: Proof and Applications
Explains the proof of the ergodic theorem and the concept of positive-recurrence in Markov chains.
Ergodic Theory: Markov Chains
Explores ergodic theory in Markov chains, discussing irreducibility and unique stationary distributions.
Discrete-Time Markov Chains: Absorbing Chains Examples
Explores examples of absorbing chains in discrete-time Markov chains, focusing on transition probabilities.
Discrete-Time Markov Chains: Absorbing Chains Examples
Covers examples of absorbing chains in discrete-time Markov chains.
Markov Chains: Reversibility and Stationary Distribution
Explores reversibility in Markov chains and its impact on the stationary distribution, highlighting the complexity of non-reversible chains.
Continuous-Time Markov Chains: Birth and Death Processes
Explores continuous-time Markov chains with a focus on birth and death processes.