MAT330 LECTURE 27 (5/11/2020): SIMULATIONS AND MARKOV CHAINS

• Announcements: This is the last lecture of the semester in which we discuss new material; the next lecture will be a revision for the Final Exam, which will be conducted remotely just like the Midterm Exam. It will be made available to you on Tuesday 5/19 at 12.00pm (noon) EDT and will be due the next day, Wednesday 5/20 at 11.59pm (midnight) EDT. More details will come by email shortly.

• Simulating a random variable with prescribed pdf (theory): Download file or watch below

• Example of simulating exponential random variable (Part I: theoretic computations): Download file or watch below

• Example of simulating exponential random variable (Part II: computer simulation): Download file or watch below

• Markov Chains (mathematical formulation and discussion): Download file or watch below

• Markov Chains (Chapman-Kolmogorov equation and long-range frequencies): Download file or watch below

• Lecture Notes (static file from above videos): PDF file

• External link 1: Recap on simulating random variables (video): Watch on YouTube

• External link 2: Recap on Markov chains (video): Watch on YouTube

• External link 3: Transition probabilities after N-steps (video): Watch on YouTube

• External link 4: Example of a Markov chain -- same one as I discuss and simulate above (video): Watch on YouTube

• External link 5: Discussion of convergence questions, with counter-examples when ergodicity fails (video): Watch on YouTube

• External link 6: Recurrent and transient states, and convergence (video, Part I): Watch on YouTube

• External link 7: Recurrent and transient states, and convergence (video, Part II): Watch on YouTube

• External link 8: Recurrent and transient states, and convergence (video, Part III): Watch on YouTube

Last updated: May 6, 2020, 8:00pm EDT