1.1 Basic concepts and classification of random processes.
1.2 Finite-dimensional distributions. Transition probabilities. Conditional expectation.
2 ¿ Discrete time processes
2.1 Examples of discrete-time processes. The simple random walk and the player's ruin. Martingales in discrete time.
2.2 Markov chains in discrete time. State classification. Stop times. limit theorems. Limit and stationary distributions.
3 - Continuous time processes
3.2 Examples of continuous-time processes with discrete state spaces. Renewal Processes. Queues and processes of birth and death. Poisson's process. Non-homogeneous Poisson process. Superposition of Poisson Processes.
3.3 Examples of processes with continuous state space. Processes with independent increments. The Brownian motion.