Statistical Sciences

LUISA BEGHIN
LUISA BEGHIN

Learning goals

General goals.
The primary educational goal of teaching is to learn the main concepts related to the theory of stochastic processes.
Students must also be able to apply the methods and be able to interpret the results.

Knowledge and understanding.
After attending the course the students know and understand the main concepts on discrete and continuous processes.

Applying knowledge and understanding.
At the end of the course the students are able to formalize real problems and to solve them by applying the specific methods of the discipline.

Making judgements.
Students develop critical skills through the application of the theory of stochastic processes.

Communication skills.
Students, through the study and performance of practical exercises, acquire the technical-scientific language of the discipline, which must be used appropriately in both the written and oral tests.

Learning skills.
Students who pass the exam have learned a method of analysis that allows them to tackle the subsequent teachings of statistical-probabilistic area.

Basic concepts of calculus and mathematical analysis. Basic knowledge of probability theory.

I part:
1. Recap of probability and measure theory
2. Markov Chains

II part (for beginners in Stochastic processes):
1. Conditioned expected values
2. Random walks
3. Martingales
4. Brownian motion
5. Stochastic integration (hints)

II part (for those who have already taken an exam in Stochastic processes):
1. Recap on conditioned expected values
2. Markov processes
3. Lévy processes

Enzo Orsingher, Luisa Beghin, Probabilità e Modelli Aleatori, 2006, Aracne Editrice

Paolo Baldi, Calcolo delle Probabilità, 2011, McGraw Hill, seconda edizione.

G.R. Grimmett and D.R. Stirzaker. Probability and Random Processes. 3rd edn, OUP, 2001

Sheldon Ross, Introduction to Probability Models, 2010, 10th edition, Elsevier

Lectures

The attendance of lectures and classes is strongly suggested

The examination consists of a written exam with questions on the topics studied during the course. A short oral exam will follow.
The students are required to answer all the questions showing that they have acquired the intuition and the technical language, and that they are able to present the topics and the proofs with all necessary details.