2023
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, English
Regime de Frequência: Presencial
Sustainable Development Goals
Learning Goals
The skills to be developed by the student:
Acquisition of fundamental theoretical concepts of stochastic processes and its application. Study of mathematical models for various random phenomena that evolve over time, discrete time and continuous time. Self-study of other models, suitable for the resolution of practical cases in which the students may encounter in the future.
The learning outcomes are:
It is intended that the students are able to build mathematical models for random phenomena that evolve over time. Students should also be able to communicate ideas and scientific knowledge in the form oral or written, involving the use and/or interpretation of knowledge of the scope of this course.
Acquisition of fundamental theoretical concepts of stochastic processes and its application. Study of mathematical models for various random phenomena that evolve over time, discrete time and continuous time. Self-study of other models, suitable for the resolution of practical cases in which the students may encounter in the future.
The learning outcomes are:
It is intended that the students are able to build mathematical models for random phenomena that evolve over time. Students should also be able to communicate ideas and scientific knowledge in the form oral or written, involving the use and/or interpretation of knowledge of the scope of this course.
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
- 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
The course is organized into theoretical-practical classes. Classes are plenary sessions based on the deduction, understanding and interpretation of the various subjects, promoting a critical attitude and scientific rigor in students. Introducing to theoretical concepts as well as exercises/examples of application, thus seeking to sensitize students to the importance of the exposed matter. Motivation of the students to go to classes as well as for the continued monitoring of the subject taught. Use, whenever possible, of statistical programs (in particular R) in various applications. The evaluation is foreseen continuous through the realization of two frequencies. There is an exame regimen available for the students that does not obtain approval by continuous evaluation or opts for evaluation in the exame regime. The student is approved in the course unit if he obtains a final grade (average of 2 frequencies/exam grade) of at least 9.5 (on a scale of 0 to 20).
Teaching Staff
- Gonçalo João Costa Jacinto [responsible]
