Simulation and Stochastic Processes
Keywords |
Classification |
Keyword |
OFICIAL |
Mathematics |
Instance: 2020/2021 - 1S ![Requerida a integração com o Moodle Ícone do Moodle](/fcup/pt/imagens/MoodleIcon)
Cycles of Study/Courses
Teaching language
Portuguese
Objectives
The main objective of the course is to introduce rigorously the main concepts of Stochastic Processes and Simulation. Those concepts and the relevant mathematical tools to their analysis in several applications will be considered in the course.
Learning outcomes and competences
In the first part of the course, some eseential concepts about Monte Carlo methods and Stochastic Processes will be consolidated. The second part of the course will be devoted to applications of the aquired knowledge using simulation in other fields of knowledge.
Working method
Presencial
Pre-requirements (prior knowledge) and co-requirements (common knowledge)
It is advised that the student had previous contact with: Probabilities and Statistics, and Real Analysis.
Program
I. Revisions on probabilities and discrete and continuous random variables.
II. Simulation and the Monte Carlo Method Statistical aspects of simulation. Simulation of data (discrete and continuous distributions): general methods, transformations and mixtures; critical use of available current generators. Monte Carlo integration and estimation of expected values. Variance reduction techniques. Monte Carlo method in statistical inference. Resampling methods.
III. Random walk. Browninan motion.
IV. Introduction to stochastic processes and its simulation. Classes of stochastic processes. Introduction to statistical analysis of signals and time series: characterization, stationarity, autocorrelation.
IV. Estimation and simulation. Modeling/simulation: Markov chains, Poisson process, random walk, birth and death processes, queuing theory.
Mandatory literature
Ross Sheldon M.;
Simulation. ISBN: 0-12-598410-3
Papoulis Athanasios;
Probability, random variables, and stochastic processes. ISBN: 0-07-048468-6
Shonkwiler Ronald W. 1942-;
Explorations in Monte Carlo methods. ISBN: 9780387878362
Law A., Kelton W.D; Simulation Modelling and Analysis, McGrawHill, 2007. ISBN: 978-0073401324
Wood Matt A.;
Python and Matplotlib essentials for scientists and engineers. ISBN: 978-1-62705-619-9
Evans Lawrence C. 1949-;
An introduction to stochastic differential equations. ISBN: 978-1-4704-1054-4
Complementary Bibliography
Ross Sheldon M.;
Introduction to probability models. ISBN: 978-0-12-375686-2
Teaching methods and learning activities
Presentation of the topics of the course and their discussion with the students.
Software
Jupyter
Python
keywords
Physical sciences > Mathematics > Applied mathematics
Physical sciences > Mathematics > Probability theory
Evaluation Type
Distributed evaluation without final exam
Assessment Components
designation |
Weight (%) |
Teste |
85,00 |
Trabalho prático ou de projeto |
15,00 |
Total: |
100,00 |
Amount of time allocated to each course unit
designation |
Time (hours) |
Estudo autónomo |
106,00 |
Frequência das aulas |
56,00 |
Total: |
162,00 |
Eligibility for exams
Score greater than 9,5 points.
Calculation formula of final grade
Final classification = t1 + t2 + tc1 + tc2
t1 = 1st test score quoted to 8,5
t2 = 2st test score quoted to 8,5
tc1 = 1st computational work quoted to 1,5
tc1 = 2st computational work quoted to 1,5
NOTE: tc1 and tc2 are obtained during class time.
These scores transit to the second season exam.
SECOND SEASON EXAM:
Final classification = er1 + er2 + tc1 + tc2
er1 = 1st exam score quoted to 8,5
er2 = 1st exam score quoted to 8,5
tc1, tc2 = tc1 and tc2 are obtained during class time.
(1) The second season exam consists of two parts corresponding to the division of matter for the tests.
(2) In the second season exam, the student can choose one or two of its parts. If he/she submits it for correction, it will replace the corresponding classification(s) obtained in the test(s).
Note: t1 and/or t2 can be divided into two parts
Classification improvement
Grade improvement will be made in the appeal examination.