Advanced Topics in Probability and Stochastic Processes
Code
9704
Academic unit
Faculdade de Ciências e Tecnologia
Department
Departamento de Matemática
Credits
6.0
Teacher in charge
Pedro José dos Santos Palhinhas Mota
Weekly hours
2
Teaching language
Português
Objectives
It is intended by studying some topics of probabilities and relevant stochastic processes in the context of the doctoral program, to enable students with the appropriate skills (in this area) in order to contribute to a successful development of the doctoral thesis.
Prerequisites
Knowledge of Probability and Statistics, Stochastic Processes, Measure Theory, Mathematical Analysis and Algebra.
Subject matter
• Review of Probability Theory
• Random Sequences
• Characteristic and moments generating functions
• Classical Limits Theorems (Law of Large Numbers and Central Limit Theorem)
• Conditioning (Conditional Expectation)
• Stochastic processes and Martingales
• Markov Processes and Discrete Time Markov Chains
• Poisson processes and renewal processes
• Stationary Processes (Time Series)
• Gaussian Processes and Wiener Process
• Ergodic processes (continuous time)
Bibliography
- Billingsley, P., Probability and measure. 3rd edition. John Wiley & Sons, 1995.
- Brockwell, P.J. and Davis, R.A., Time Series: theory and methods. Springer, 1991.
- Durret, R., Essential of Stochastic Processes. Springer, 2012.
- Kallenberg O., Foundations of Modern Probability. Springer, 1997.
- Shiryaev, A.N., Probability. 2nd Edition. Springer, 1996.
- Williams, D., Probability with Martingales. Cambridge University Press, 1991.
Teaching method
The classes work in a practical theoretical regime, with a tutorial component.
Evaluation method
The evaluation is carried out by carrying out individual assignments on the form of a written report.