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Institutionernas kurser för doktorander

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Kursplan för

Läsår
MVE250 - Probability and random processes, advanced level
 
Kursplanen fastställd 2009-03-01 av programansvarig (eller motsvarande)
Ägare: MPCOM
7,5 Poäng
Betygskala: UG - Underkänd, Godkänd
Utbildningsnivå: Avancerad nivå
Huvudområde: Elektroteknik, Matematik
Institution: 11 - MATEMATISKA VETENSKAPER


Undervisningsspråk: Engelska

Modul   Poängfördelning   Tentamensdatum
Lp1 Lp2 Lp3 Lp4 Sommarkurs
0108 Muntlig tentamen 7,5 hp Betygskala: UG   7,5 hp    

I program

MPSYS SYSTEMS, CONTROL AND MECHATRONICS, MSC PROGR - Special research and PhD course, Årskurs 2 
MPCOM COMMUNICATION ENGINEERING, MSC PROGR, Årskurs 2 (valbar)

Examinator:

Forskarassistent  Jenny Jonasson



  Gå till kurshemsida

Behörighet:

För kurser inom Chalmers utbildningsprogram gäller samma behörighetskrav som till de(t) program kursen ingår i.

Kursspecifika förkunskaper

A basic course in probability or mathematical statistics

Software skills

MATLAB programming skills or equivalent.

Syfte

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

Lärandemål (efter fullgjord kurs ska studenten kunna)

* 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 fundametal 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.


 

Innehåll

"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.

Litteratur

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

Examination

Oral examination.


Sidansvarig Publicerad: må 13 jul 2020.