Continuous Time Markov Chains

This lecture covers the concept of continuous time Markov chains, defined on a finite state space, with initial probabilities, jump rates, and jump probabilities. The Markov chain stays at a state for an exponential amount of time before jumping to another state. Two constructions are presented, one based on independent sequences of exponential random variables and the other on Poisson processes. The lecture also introduces Q-matrices, which are matrices satisfying specific conditions related to the Markov chain transitions.