Simulation and Stochastic Processes

Code:

M3014

Acronym:

M3014

Level:

300

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2017/2018 - 2S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Bachelor in Mathematics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:B	0	Official Study Plan	3	-	6	56	162
L:CC	0	Plano de estudos a partir de 2014	2	-	6	56	162
			3
L:F	3	Official Study Plan	2	-	6	56	162
			3
L:G	5	study plan from 2017/18	3	-	6	56	162
L:M	44	Official Study Plan	2	-	6	56	162
			3
L:Q	0	study plan from 2016/17	3	-	6	56	162

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.