Measure theory and stochastic processes

Code:

PDEEC0015

Acronym:

MTSP

Keywords
Classification	Keyword
OFICIAL	Electrical and Computer Engineering

Instance: 2013/2014 - 2S

Active?	Yes
E-learning page:	https://moodle.fe.up.pt/
Responsible unit:	Department of Electrical and Computer Engineering
Course/CS Responsible:	Doctoral Program in Electrical and Computer Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
PDEEC	2	Syllabus since 2007/08	1	-	7,5	70	202,5

Teaching language

English

Objectives

To provide graduate students in the area of, control theory and other related disciplines with a solid background in random processes and in estimation, filtering and prediction theory.

Learning outcomes and competences

At the end of the course, it is expected that the students are able to:

- understand scientific literature in which stochastic processes, with discrete and with continuous sample spaces, are formally defined.

- Describe, in a formal and rigorous way, the stochastic processes used in specific applications.

- Know, understand and can apply the main methods studied for estimation, prediction and filtering.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

- Linear algebra and calculus at a level of an engineering first degree.

 

- familiarity with both discrete-time and continuous-time processes described by time difference or differential equations. 

Program

1 - Probability spaces
 2 - Construction of probabilities spaces
 3 - Measurable functions
 4 - Integration and Expectation
  5 - Lq Probability spaces
   6 - Independence:
    7 - The Fubini theorem.
    8 - The Radon Nikodin derivative
    9 - Random variables
     10 - Random Vectors
      11 - Useful Inequalities
       12 - Convergence of random variables
        13 - Random walk
        14 - Filtrations
        15 - Estimation and Prediction

16 - Kalman Filter

17- Stochastic Realization Theory

      

 

      

Mandatory literature

Katayama, Tohru 1942-; Subspace methods for system identification. ISBN: 1-85233-981-0
Grigoriu, Mircea; Stochastic calculus. ISBN: 3-7643-4242-0
J. F. C. Kingman , S. J. Taylor ; Introduction to Measure and Probability , Cambridge University Press, 2008. ISBN: ISBN-10: 0521090326 | ISBN-13: 978-0521090322
Sofia Lopes, F. A. C. C. Fontes , Margarida Ferreira, Maria Do Rosário De Pinho ; Notes on Measure Theory, 2011

Teaching methods and learning activities

There will be expository lectures in the end of which a list of problems are proposed. Such lectures are followed by discussion classes to treat problems assigned on the subject

Software

Matlab

keywords

Physical sciences > Mathematics > Probability theory
Physical sciences > Mathematics > Applied mathematics > Engineering mathematics

Evaluation Type

Distributed evaluation without final exam

Assessment Components

Designation	Weight (%)
Trabalho escrito	100,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	120,00
Total:	120,00

Eligibility for exams

Presence in more than half of the lectures.

Calculation formula of final grade

Average of the grades given to each homework.

Examinations or Special Assignments

Students will have to do different homework that should be returned within a week after being assigned.