2025
Stochastic Processes and Applications
Name: Stochastic Processes and Applications
Code: MAT13615M
6 ECTS
Duration: 15 weeks/156 hours
Scientific Area:
Mathematics
Teaching languages: Portuguese
Languages of tutoring support: Portuguese
Sustainable Development Goals
Learning Goals
The learning outcomes are:
In general, aims to provide fundamental theoretical concepts for analyzing discrete and continuous time phenomena, subject to uncertainties.
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 skills to be developed by the student:
It is intended that the students are able to build mathematical models for random phenomena that evolve over time.
Acquisition of fundamental theoretical concepts of stochastic processes, as well as its importance in to application to real life phenomena.
In general, aims to provide fundamental theoretical concepts for analyzing discrete and continuous time phenomena, subject to uncertainties.
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 skills to be developed by the student:
It is intended that the students are able to build mathematical models for random phenomena that evolve over time.
Acquisition of fundamental theoretical concepts of stochastic processes, as well as its importance in to application to real life phenomena.
Contents
General concepts of Stochastic Processes.
Martingales and applications.
Discrete-time Markov chains.
Homogeneous, nonhomogeneous and compound Poisson processes.
Birth and death processes.
Introduction to queueing theory.
Renewal processes.
Monte Carlo simulation methods.
Martingales and applications.
Discrete-time Markov chains.
Homogeneous, nonhomogeneous and compound Poisson processes.
Birth and death processes.
Introduction to queueing theory.
Renewal processes.
Monte Carlo simulation methods.
Teaching Methods
Lectures and practical classes taught in the blackboard.
Introduction to theoretical concepts and practical exercises using examples in several areas,
thus seeking to sensitize students to the importance of the exposed topics.
To privilege continuous evaluation, with 2 tests (50%) and 2 individual or group homeworks (50%).
Evaluation under examination: a final exam (50%) and an application homework (50%).
Introduction to theoretical concepts and practical exercises using examples in several areas,
thus seeking to sensitize students to the importance of the exposed topics.
To privilege continuous evaluation, with 2 tests (50%) and 2 individual or group homeworks (50%).
Evaluation under examination: a final exam (50%) and an application homework (50%).
Certificações
