Stochastic Processes, 6 credits (TAMS32)

Stokastiska processer, 6 hp

Main field of study

Mathematics Applied Mathematics Electrical Engineering

Level

Second cycle

Course type

Programme course

Examiner

Torkel Erhardsson

Director of studies or equivalent

Nils-Hassan Quttineh

Available for exchange students

Yes
Course offered for Semester Period Timetable module Language Campus VOF
6MMAT Mathematics, Master's Programme 1 (Autumn 2018) 1 1 Swedish/English Linköping o
6CDDD Computer Science and Engineering, M Sc in Engineering 7 (Autumn 2018) 1 1 Swedish/English Linköping v
6CIEI Industrial Engineering and Management - International, M Sc in Engineering - German 7 (Autumn 2018) 1 1 Swedish/English Linköping v
6CIEI Industrial Engineering and Management - International, M Sc in Engineering - Spanish 7 (Autumn 2018) 1 1 Swedish/English Linköping v
6CIEI Industrial Engineering and Management - International, M Sc in Engineering - French 7 (Autumn 2018) 1 1 Swedish/English Linköping v
6CIEI Industrial Engineering and Management - International, M Sc in Engineering - Chinese 7 (Autumn 2018) 1 1 Swedish/English Linköping v
6CIEI Industrial Engineering and Management - International, M Sc in Engineering - Japanese 7 (Autumn 2018) 1 1 Swedish/English Linköping v
6CIII Industrial Engineering and Management, M Sc in Engineering 7 (Autumn 2018) 1 1 Swedish/English Linköping v
6CITE Information Technology, M Sc in Engineering 7 (Autumn 2018) 1 1 Swedish/English Linköping v
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Applied Mathematics) 7 (Autumn 2018) 1 1 Swedish/English Linköping o
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 7 (Autumn 2018) 1 1 Swedish/English Linköping v
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Financial Mathematics) 7 (Autumn 2018) 1 1 Swedish/English Linköping o
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Applied Mathematics) 7 (Autumn 2018) 1 1 Swedish/English Linköping o
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 7 (Autumn 2018) 1 1 Swedish/English Linköping v
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Financial Mathematics) 7 (Autumn 2018) 1 1 Swedish/English Linköping o
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Applied Mathematics) 7 (Autumn 2018) 1 1 Swedish/English Linköping o
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 7 (Autumn 2018) 1 1 Swedish/English Linköping v
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Financial Mathematics) 7 (Autumn 2018) 1 1 Swedish/English Linköping o
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Applied Mathematics) 7 (Autumn 2018) 1 1 Swedish/English Linköping o
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 7 (Autumn 2018) 1 1 Swedish/English Linköping v
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Financial Mathematics) 7 (Autumn 2018) 1 1 Swedish/English Linköping o
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Applied Mathematics) 7 (Autumn 2018) 1 1 Swedish/English Linköping o
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 7 (Autumn 2018) 1 1 Swedish/English Linköping v
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering (Financial Mathematics) 7 (Autumn 2018) 1 1 Swedish/English Linköping o
6CYYY Applied Physics and Electrical Engineering, M Sc in Engineering 7 (Autumn 2018) 1 1 Swedish/English Linköping v
6CYYY Applied Physics and Electrical Engineering, M Sc in Engineering (Applied Mathematics) 7 (Autumn 2018) 1 1 Swedish/English Linköping o
6CYYY Applied Physics and Electrical Engineering, M Sc in Engineering (Financial Mathematics) 7 (Autumn 2018) 1 1 Swedish/English Linköping o

Main field of study

Mathematics, Applied Mathematics, Electrical Engineering

Course level

Second cycle

Advancement level

A1X

Course offered for

  • Master's Programme in Mathematics
  • Computer Science and Engineering, M Sc in Engineering
  • Industrial Engineering and Management - International, M Sc in Engineering
  • Industrial Engineering and Management, M Sc in Engineering
  • Information Technology, M Sc in Engineering
  • Applied Physics and Electrical Engineering - International, M Sc in Engineering
  • Applied Physics and Electrical Engineering, M Sc in Engineering

Entry requirements

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.

Prerequisites

Basic courses in probability. Linear algebra and multivariate analysis. Transform theory is helpful, but not required.

Intended learning outcomes

In broad terms, the course treats statistical models and methods for randomly varying quantities which are also functions of time. These are fundamental for the advanced study of telecommunications theory, signal theory, control theory, robotics, and many important phenomena in biology, physics, computer networks, and economy. After a completed course the student is expected to be able to:

  • describe the basic concepts and theorems in the theory of stochastic processes, e.g., expectation and autocovariance function and spectral density.
  • describe important classes of stochastic processes, e.g., the Wiener process, martingales, wide sense stationary processes, and Markov chains, and their special properties.
  • make use of stochastic processes to construct relevant models for randomly varying quantities which are functions of time.
  • carry out important computations for stochastic processes, such as linear time invariant filtration, and prediction of the values of a process at unobserved times.
  • understand and assess models based on stochastic processes and analyses of such models occurring in other undergraduate courses, or the media.

Course content

Multivariate distributions, in
particular the multivariate normal distribution. Conditioning and
conditional expectation. The moment generating function. Stochastic
processes: basic properties and examples. Expectation function,
autocovariance function, cross covariance function. The Poisson
process and the Wiener process. Martingales in discrete time.
Stationary and wide sense stationary processes. Gaussian processes. Mean square
convergence and the mean square integral. Linear time invariant filtering.
Spectral densities. ARMA processes. Prediction. Markov chains in
discrete and continuous time.

Teaching and working methods

Lectures and tutorials. Home assignments which are not mandatory but give bonus points at the written examination.

Examination

TEN1Written ExaminationU, 3, 4, 56 credits

Grades

Four-grade scale, LiU, U, 3, 4, 5

Other information

Supplementary courses: Probability theory, advanced course. Stochastic processes applied to finance. Control theory. Biomedical signal processing. Classification and decision support.

Department

Matematiska institutionen

Director of Studies or equivalent

Nils-Hassan Quttineh

Examiner

Torkel Erhardsson

Course website and other links

http://courses.mai.liu.se/GU/TAMS32

Education components

Preliminary scheduled hours: 48 h
Recommended self-study hours: 112 h

Course literature

Books
Roy D. Yates & David J.Goodman, (2005) Probability and stochastic processes. A Friendly introduction for electrical and computer engineers 2nd ed John Wiley
Other

Books

Roy D. Yates & David J.Goodman, (2005) Probability and stochastic processes. A Friendly introduction for electrical and computer engineers 2nd ed John Wiley

Other

TEN1 Written Examination U, 3, 4, 5 6 credits

Course syllabus

A syllabus has been established for each course. The syllabus specifies the aim and contents of the course, and the prior knowledge that a student must have in order to be able to benefit from the course.

Timetabling

Courses are timetabled after a decision has been made for this course concerning its assignment to a timetable module. A central timetable is not drawn up for courses with fewer than five participants. Most project courses do not have a central timetable.

Interrupting a course

The vice-chancellor’s decision concerning regulations for registration, deregistration and reporting results (Dnr LiU-2015-01241) states that interruptions in study are to be recorded in Ladok. Thus, all students who do not participate in a course for which they have registered must record the interruption, such that the registration on the course can be removed. Deregistration from a course is carried out using a web-based form: www.lith.liu.se/for-studenter/kurskomplettering?l=sv. 

Cancelled courses

Courses with few participants (fewer than 10) may be cancelled or organised in a manner that differs from that stated in the course syllabus. The board of studies is to deliberate and decide whether a course is to be cancelled or changed from the course syllabus. 

Regulations relating to examinations and examiners 

Details are given in a decision in the university’s rule book: http://styrdokument.liu.se/Regelsamling/VisaBeslut/622678.

Forms of examination

Examination

Written and oral examinations are held at least three times a year: once immediately after the end of the course, once in August, and once (usually) in one of the re-examination periods. Examinations held at other times are to follow a decision of the board of studies.

Principles for examination scheduling for courses that follow the study periods:

  • courses given in VT1 are examined for the first time in March, with re-examination in June and August
  • courses given in VT2 are examined for the first time in May, with re-examination in August and October
  • courses given in HT1 are examined for the first time in October, with re-examination in January and August
  • courses given in HT2 are examined for the first time in January, with re-examination at Easter and in August.

The examination schedule is based on the structure of timetable modules, but there may be deviations from this, mainly in the case of courses that are studied and examined for several programmes and in lower grades (i.e. 1 and 2). 

  • Examinations for courses that the board of studies has decided are to be held in alternate years are held only three times during the year in which the course is given.
  • Examinations for courses that are cancelled or rescheduled such that they are not given in one or several years are held three times during the year that immediately follows the course, with examination scheduling that corresponds to the scheduling that was in force before the course was cancelled or rescheduled.
  • If teaching is no longer given for a course, three examination occurrences are held during the immediately subsequent year, while examinations are at the same time held for any replacement course that is given, or alternatively in association with other re-examination opportunities. Furthermore, an examination is held on one further occasion during the next subsequent year, unless the board of studies determines otherwise.
  • If a course is given during several periods of the year (for programmes, or on different occasions for different programmes) the board or boards of studies determine together the scheduling and frequency of re-examination occasions.

Registration for examination

In order to take an examination, a student must register in advance at the Student Portal during the registration period, which opens 30 days before the date of the examination and closes 10 days before it. Candidates are informed of the location of the examination by email, four days in advance. Students who have not registered for an examination run the risk of being refused admittance to the examination, if space is not available.

Symbols used in the examination registration system:

  ** denotes that the examination is being given for the penultimate time.

  * denotes that the examination is being given for the last time.

Code of conduct for students during examinations

Details are given in a decision in the university’s rule book: http://styrdokument.liu.se/Regelsamling/VisaBeslut/622682.

Retakes for higher grade

Students at the Institute of Technology at LiU have the right to retake written examinations and computer-based examinations in an attempt to achieve a higher grade. This is valid for all examination components with code “TEN” and "DAT". The same right may not be exercised for other examination components, unless otherwise specified in the course syllabus.

Retakes of other forms of examination

Regulations concerning retakes of other forms of examination than written examinations and computer-based examinations are given in the LiU regulations for examinations and examiners, http://styrdokument.liu.se/Regelsamling/VisaBeslut/622678.

Plagiarism

For examinations that involve the writing of reports, in cases in which it can be assumed that the student has had access to other sources (such as during project work, writing essays, etc.), the material submitted must be prepared in accordance with principles for acceptable practice when referring to sources (references or quotations for which the source is specified) when the text, images, ideas, data, etc. of other people are used. It is also to be made clear whether the author has reused his or her own text, images, ideas, data, etc. from previous examinations.

A failure to specify such sources may be regarded as attempted deception during examination.

Attempts to cheat

In the event of a suspected attempt by a student to cheat during an examination, or when study performance is to be assessed as specified in Chapter 10 of the Higher Education Ordinance, the examiner is to report this to the disciplinary board of the university. Possible consequences for the student are suspension from study and a formal warning. More information is available at https://www.student.liu.se/studenttjanster/lagar-regler-rattigheter?l=sv.

Grades

The grades that are preferably to be used are Fail (U), Pass (3), Pass not without distinction (4) and Pass with distinction (5). Courses under the auspices of the faculty board of the Faculty of Science and Engineering (Institute of Technology) are to be given special attention in this regard.

  1. Grades U, 3, 4, 5 are to be awarded for courses that have written examinations.
  2. Grades Fail (U) and Pass (G) may be awarded for courses with a large degree of practical components such as laboratory work, project work and group work.

Examination components

  1. Grades U, 3, 4, 5 are to be awarded for written examinations (TEN).
  2. Grades Fail (U) and Pass (G) are to be used for undergraduate projects and other independent work.
  3. Examination components for which the grades Fail (U) and Pass (G) may be awarded are laboratory work (LAB), project work (PRA), preparatory written examination (KTR), oral examination (MUN), computer-based examination (DAT), home assignment (HEM), and assignment (UPG).
  4. Students receive grades either Fail (U) or Pass (G) for other examination components in which the examination criteria are satisfied principally through active attendance such as other examination (ANN), tutorial group (BAS) or examination item (MOM).

The examination results for a student are reported at the relevant department.

Regulations (apply to LiU in its entirety)

The university is a government agency whose operations are regulated by legislation and ordinances, which include the Higher Education Act and the Higher Education Ordinance. In addition to legislation and ordinances, operations are subject to several policy documents. The Linköping University rule book collects currently valid decisions of a regulatory nature taken by the university board, the vice-chancellor and faculty/department boards.

LiU’s rule book for education at first-cycle and second-cycle levels is available at http://styrdokument.liu.se/Regelsamling/Innehall/Utbildning_pa_grund-_och_avancerad_niva. 

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