Mathematics

General objectives: to acquire basic knowledge in stochastic process theory and in stochastic modeling of real phenomena. Specific objectives: Knowledge and understanding: at the end of the course the student will have acquired the basic notions and results concerning stochastic processes in discrete and continuous time, on discrete structures such as graphs or on continuous spaces. Apply knowledge and understanding: at the end of the course the student will be able to model the temporal evolution of various real phenomena through stochastic processes, to analyze the stationarity and / or temporal reversibility of stochastic processes, to calculate probabilities of absorption and expected absorption times, to simulate stochastic processes and to estimate the rate of convergence at equilibrium. Critical and judgmental skills: the student will have the basis to study stochastic dynamic systems and acquire the ability to evaluate the goodness of a model compared to others in the modeling of real phenomena. Communication skills: having to take an oral theory test, students will develop the communication skills necessary to expose the mathematical theory and the various models considered in the course. Learning skills: the acquired knowledge will allow a more in-depth study of stochastic processes both on discrete and continuous spaces, helping the student to study other courses such as stochastic calculus.