Lectures related to Ergodic Theory: Markov Chains

Limiting Distribution and Ergodic Theorem

Explores limiting distribution in Markov chains and the implications of ergodicity and aperiodicity on stationary distributions.

Markov Chains: Ergodic Chains Examples

Covers stochastic models for communications, focusing on discrete-time Markov chains.

Markov Chains: Ergodic Chains Examples

Covers stochastic models for communications, focusing on discrete-time Markov chains.

Coupling of Markov Chains: Ergodic Theorem

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

Markov Chains: Ergodicity and Stationary Distribution

Explores ergodicity and stationary distribution in Markov chains, emphasizing convergence properties and unique distributions.

Markov Chains: PageRank Algorithm

Explores the PageRank algorithm within Markov chains, emphasizing ergodicity and convergence for web page ranking.

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.

Theory of MCMC

Covers the theory of Markov Chain Monte Carlo (MCMC) sampling and discusses convergence conditions, transition matrix choice, and target distribution evolution.

Recurrence and transience in markov chains

Explores the concepts of recurrence and transience in continuous time Markov chains.

Continuous-Time Markov Chains: Reversible Chains

Covers reversible continuous-time Markov chains and their properties.

Classification and Recurrence/Transience

Explores classification, communication, and irreducibility in Markov chains.

Markov Chains: Ergodic Chains Examples

Covers stochastic models for communications, focusing on discrete-time Markov chains.

Ergodic Theorem: Proof and Applications

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

Applied Probability & Stochastic Processes

Covers applied probability, Markov chains, and stochastic processes, including transition matrices, eigenvalues, and communication classes.

Continuous-Time Markov Chains: Reversible Chains

Covers Mod.7 on continuous-time Markov chains, focusing on reversible chains and their applications in communication systems.

Continuous-Time Markov Chains: Reversible Chains

Covers continuous-time Markov chains, focusing on reversible chains and their properties.

Invariant Measures: Properties and Applications

Covers the concept of invariant measures in Markov chains and their role in analyzing irreducible recurrent processes.

Discrete-Time Markov Chains: Reversible Chains

Covers reversible discrete-time Markov chains in communication models.

Markov Chains: Homogeneous Processes and Stationary Distributions

Explores Markov chains, focusing on homogeneous processes and stationary distributions, with practical exercises.

Continuous Time Markov Chains

Covers the basic theory for continuous time Markov chains and discusses communication, hitting probabilities, recurrence, and transience.