1.Stochastic Process 2.Poisson Process 3.Markov Chain
At the end, students are expected to have acquired a fundamental knowledge on stochastic processes and on applications of the different types of stochastic processes to the study of concrete examples arising from different fields of applications.
1. Basic concepts, properties and classification of general stochastic processes. 2. Poisson processes: axiomatic and axiomatic derivations of Poisson processes. 3. Discrete-time Markov chains: Transition probability matrices and transition probabilities, Chapman-Kolmogorov equation, classification of states, limit distributions. 4. Continuous-time Markov chains: birth and death processes, Kolmogorov equations, limit theorems. 5. Examples of stochastic processes and applications.
Main reading: D. Muller: Processos Estocásticos e Aplicações, Colecção Económicas, II Série, Nº 3, Almedina, Coimbra, 2007.
Continuous assessment is privileged: 2 or 3 digital written documents (e-folios) during the semester (40%) and a
presence-based final exam (p-folio) in the end of the semester (60%). In due time, students can alternatively choose to perform one
final presence-based exam (100%).
Students are recommended to have previously knowledge in the Elements of Probability and Statistics curricular unit.