Section outline

  • Lecture 17 (22.04.26) - Transition times and embedded MC: definition and properties (theorem). Graphical construction: construction of t-MC via indepedent marked Poisson Processes. Examples: birth and death process; random walks; interacting particle systems (exclusion process, contact process). 
    Lecture 18 (23.04.26) - Invariant measure of t-Markoc chains. Recurrence/transience and positive recurrence of t-Markov chains. Invariant measures: existence, characterization, and uniqueness of invariant distribution. Theorem of convergence of t-Markov chains. Space of trajectories of t-Markov chains: cadlag space D[0,T], metric and Skorohod topology (main properties and results).