Knowledge and understanding of the fundamental elements of probability theory for the description of univariate and multivariate random phenomena, of the basics in the theory of stochastic processes, of the usefulness of stochastic processes for the description of random phenomena in biology, finance and engineering.
Applying knowledge and understanding
Understanding of the probabilistic models as useful instruments for research in applied sciences an ability to use stochastic processes in order to describe random phenomena.
Making judgements on the appropriate probabilistic models and methods to be used for analyzing a specific dataset and on the interpretation of the experimental results.
Communication skills in order to present a probabilistic model, including both the methodology and the expected results, in a consistent and convincing way.
Learning skills based on the prerequisites that are required for understanding autonomously a report on the application of the theory of stochastic processes and for learning more advanced probabilistic procedures.
More information on the degree course are available on https://www.uniud.it/it/didattica/info-didattiche/regolamento-didattico-del-corso/LM-matematica/all-B2/anno-accademico-202-2022/view
1) Complements on elementary probability; 2) Introduction to stochastic processes; 3) Discrete-time Markov chains; 4) Poisson processes; 5) Discrete-time martingales; 6) Brownian motion; 7) Hidden Markov models.
1) Bosq, D., Nguyen, H.T. (1996). A course in stochastic processes: stochastic models and statistical inference. Kluwer;
2) Cınlar, E. (2011). Probability and stochastics. Springer;
3) Kopp, E. (2011). From measures to Itô integrals. Cambridge University Press 4) Ross, S. M. (1996). Stochastic processes. Wiley.