Students are assumed to have taken courses on basic statistics and probability calculus.

The course objectives are that students develop the following competences: 1. Understanding the the theoretical basis and the basic properties of several fundamental stochastic processes. 2. Applying the acquired knowledge to formulate and solve problems in various application areas. 1. Capacity for analysis and synthesis. 2. Problem solving. 3. Critical Thinking.

1. The Poisson process. 1.1. Introduction and motivation; distribution of interarrival and waiting times; conditional distribution of arrival times. 1.2. Extensions and applications; non-homogeneous, compounded and conditional Poisson processes. 2. Renewal processes. 2.1. Introduction and motivation; Wald's equation; limit theorems. 2.2. The renewal theorem and applications; random incidence. 3. Discrete-time Markov chains. 3.1. Introduction and motivation; n-step transition probabilities; Chapman-Kolmogorov equations; Markov property; Joint distribution. 3.2. Long-run behaviour: numerical exploration; simulation. 3.3. Limiting distribution; stationary distributions; relation with eigenvalues; limit theorem for regular chains. 3.4. Irreducible chains; recurrence and transience; classification of states; canonical decomposition; limit theorem for finite irreducible chains. 3.5. Periodicity; ergodic chains; fundamental limit theorem for ergodic chains. 4. Continuous-time Markov chains. 4.1. Introduction and motivation; Birth-death processes; transition rates; generating matrix; transition times and probabilities; Kolmogorov equations. 4.2. Limiting distribution; stationary distributions; limit theorems. 4.3. Applications; queueing models.

Theory (3 ECTS). Lectures. Practice (3 ECTS). Problem solving classes.