Simulation and Stochastic Processes
Keywords |
Classification |
Keyword |
OFICIAL |
Mathematics |
Instance: 2017/2018 - 2S ![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. Ito's calculus /time permiting).
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
Evaluation Type
Distributed evaluation with final exam
Assessment Components
designation |
Weight (%) |
Exame |
85,00 |
Trabalho prático ou de projeto |
15,00 |
Total: |
100,00 |
Eligibility for exams
(1) A student may be exempted from final exam by doing two tests, each quoted to ten values, realized during the semester. The student is approved provided he/she gets a grade equal or superior to 10 (= sum of the marks obtained in the tests), with a minimum of four (4) values in each test.
(2) A student who goes to the final exam gets the mark here obtained being point (1) ignored.
Calculation formula of final grade
Final mark = 85% of the exam + 15% of the average of the two computational works.
REMARK: The 15% corresponding to two computational works are obtained during the course. Thus,
(i) the exam is 85% of the final mark,
(ii) the supplementary exam is 85% of the final classification,
(iii) the improvement exam is 85% of the final mark.
Classification improvement
Only the exam component.