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

The evaluation will be made in accordance with paragraph 11 of article 110 of the RAUE, considering the 2 evaluation regimes foreseen: Continuous (with 2 frequencies) or Final (per Exam). The final grade (NF), for students who obtain at least 8.0 points, in each of the frequencies, will be obtained according to the following weighting NF=0.50*F1+0.50*F2, where: F1 = Grade in the 1st frequency (50%). F2 = Grade in the 2nd frequency (50%). If the NF result is greater than or equal to 9.5, even with a grade lower than 8.0 in the 2nd frequency, the classification of the normal season will be 9 values. The use of AI tools is allowed in this course as technical, analytical and learning support, as long as students understand, validate and take full responsibility for the results produced. The misuse of sources, data or results constitutes a serious violation of academic integrity. It is unacceptable to use AI in assessments or exams without authorization. Misuse will be classified as academic fraud under Article 119 of the Academic Regulations (Code of Conduct, Fraud and Plagiarism). In case of plagiarism, the test will be invalidated and participation will be made superiorly. If deemed necessary to verify the extent to which the student has developed the knowledge and skills foreseen for the curricular unit, the student may be called for an oral test, under the terms of paragraph 13 of article 110 of the Academic Regulation of the University of Évora, and the conditions provided for in paragraph 4 of article 116 and paragraph 1 of article 118 of the same Regulation are ensured.

Teaching Staff

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