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Syllabus for

Academic year
MVE251 - Probability and random processes, advanced level
 
Syllabus adopted 2012-02-21 by Head of Programme (or corresponding)
Owner: MPCOM
7,5 Credits
Grading: UG - Fail, pass
Education cycle: Second-cycle
Major subject: Electrical Engineering, Mathematics
Department: 11 - MATHEMATICAL SCIENCES


Teaching language: English
Open for exchange students
Block schedule: C

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0112 Examination 6,0 c Grading: UG   6,0 c   18 Dec 2012 pm V,  04 Apr 2013 pm V,  21 Aug 2013 pm V
0212 Project 1,5 c Grading: UG   1,5 c    

In programs

MPCOM COMMUNICATION ENGINEERING, MSC PROGR, Year 2 (elective)
MPSYS SYSTEMS, CONTROL AND MECHATRONICS, MSC PROGR, Year 2 (elective)
MPSYS SYSTEMS, CONTROL AND MECHATRONICS, MSC PROGR, Year 1 (elective)

Examiner:

Professor  Serik Sagitov


Replaces

MVE250   Probability and random processes, advanced level


  Go to Course Homepage

Eligibility:

For single subject courses within Chalmers programmes the same eligibility requirements apply, as to the programme(s) that the course is part of.

Course specific prerequisites

A basic course in probability or mathematical statistics.
MATLAB programming skills or equivalent.

Aim

Students will master the basic concepts of probability and random processes in depth in order to understand scientific papers and produce research themselves.

Learning outcomes (after completion of the course the student should be able to)

* understand mathematically oriented scientific papers in control theory and signal processing

* handle the concepts of probability theory and random processes in a mathematically satisfactory way in research.

* be able to comprehend a mathematical text and extract the relevant
information which in this course includes


(i) the fundamental theory that and the basis for a probability space and how this is connected to the definition of random variables.


(ii) different modes of convergence.


(iii) the properties and uses of conditional expectation.


(iv) the Markov property and a thorough description of the properties of Markov processes.


(v) identification of a process that has the martingale property and its
connection to convergence.


(vi) different random processes


(vii) stationary processes, their spectral representations and the ergodic theorem.

Content

"Events and their probabilities."
To be able to deal with randomness in research a more precise definition of
probability measures is required than is usually given in the undergraduate
course.
"Random variables"
The precise definition of probability measures makes it possible to introduce
random variables in a proper way.
"Convergence of random variables"
Convergence is a tool to distinguish basic properties from specifics in the
situation at hand. Depending on the application different modes of convergence are relevant such as convergence in law, in probability, in quadratic mean and with probability one.
"Markov chains"
Random processes are characterized by the way stochastic dependence is
handled. Markov chains uses a state which includes all information which is
needed to predict the future.
"Stationary processes"
When the stationarity property holds Fourier analysis is a useful tool to
handle dependence.
"Martingales"
The martingale property of random processes is useful when proving convergence theorem.

Organisation

Discussions, projects, problem sessions.

Literature

Geoffrey Grimmet and David Stirzaker: "Probability and random processes"
Oxford University Press Third editionb 2001, Oxford UK.

Examination

The assessment is based on projects, home assignments, and a written examination.


Page manager Published: Mon 28 Nov 2016.