2025

Stochastic Processes

Name: Stochastic Processes
Code: MAT13639L
6 ECTS
Duration: 15 weeks/156 hours
Scientific Area: Mathematics

Teaching languages: Portuguese
Languages of tutoring support: Portuguese
Regime de Frequência: Presencial

Sustainable Development Goals

Learning Goals

The course aims to provide students with fundamental theoretical concepts for analyzing phenomena that evolve over time, in discrete and continuous time, and are subject to uncertainty. Specifically, it covers the most common processes, such as Markov chains, with discrete and continuous parameter space.

By completing the course, students will be able to identify the type of stochastic process that best suits each context, adapt them to that context, apply them, draw conclusions, and interpret them critically.

Contents

1. General concepts of stochastic processes:
- Properties and classification;
2. Discrete-time Markov chain
- Transition probability matrices;
- Chapman-Kolmogrov equations;
- Classification of states;
- Limiting theorems;
- Simple branching processes;
3. Poisson processes:
- Axiomatic;
- Waiting times in Poisson processes;
4. Continuous-time Markov chain.
- Birth-Death processes
- Introduction to queueing theory

Teaching Methods

Theoretical and practical classes taught on the board and using slides or other materials.
Introduction of theoretical concepts and application exercises using examples from various fields, thus aiming to raise students' awareness of the importance of the material presented.
Promotion of independent work, and in pairs, of theoretical and practical exercises on the program content.
Students will be encouraged to use the free software RStudio, or other software that may prove more appropriate, to solve and/or validate the proposed exercises.

Assessment

Continuous evaluation: Students will be evaluated through two tests, each weighing 50%, where the minimum grade for each test is 7 points. If this criterion is met, but the average score of both tests is less than 9.5 points, students will still have to take a retake exam. If students withdraw from the continuous assessment, they will also have to take a regular exam and a supplementary exam.

Non-continuous evaluation: In this case, students will have to take a regular exam and a supplementary exam.

All students will also take supplementary, special and extraordinary exams, according to the rules established by the RAUE

Teaching Staff

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