Stationary Stochastic Processes

News

• The first lecture of the course is on Monday 18/3 at 13:00-15:00 in room MA04

Course contents

Stochastic processes find applications in a wide variety of fields, and offer a refined and powerful framework to examine and analyze various signals. This course is aimed at introducing the basic theory of stochastic processes, as well as to show how the theory can find applications in a variety of fields.

The course consist of lectures, tutorials, computer exercises, and an exam.

Higher education credits: 7,5 Level: G2
Language of instruction: This course is offered in English.
Recommended prerequisites: A basic course in mathematical statistics and knowledge in complex and linear analysis.
Assessment: Written exam and compulsory computer exercises. During the exam, one is allowed to bring the table of formulas and a pocket calculator.
Literature: Stationary stochastic processes by G. Lindgren, H. Rootzén, and M. Sandsten. This booklet can be bought from the course secretary. The problem booklet and the table of formulas can be downloaded here and here. You might also find the following study questions useful.
Schedule: The course starts on Monday, March 18th, at 13:00-15:00 in room MA04. Detailed schedule for lectures and tutorials can be found here. Note that there are no lectures in weeks 13 and 14. Tutorials are offered on Tuesdays 10-12 and 13-15 (MH:362B), and Fridays 10-12 and 13-15 (MH:362B). You are welcome to attend as many of these sessions as you prefer.
Exam: The final exam is held on Thursday, May 30th, at 08.00-13.00, in Vic:3A-C. A collection of old exams can be found here.
Lecture slides from the course taught by Prof. Andreas Jakobsson in Spring 2012 may be downloaded here.

People

Lecturer: Naveed R. Butt
Tutorials: Per Möller, Magnus Håkansson
Computer exercises: Gustaf Gillander, Magnus Håkansson, Hilda Lindvall,
Course secretary: Maria Lövgren.

Preliminary schedule

Date	Lecture	Reading instructions	Problems
18/3	Introduction and overview.	Ch 1.1-1.4, 2.1-2.5	201-208.
20/3	Moment functions. Stationarity.	Ch. 2.1-2.5	209-214.
9/4	Ergodicity. Estimation.	Ch. 2.1-2.5	215-221.
10/4	Spectral representation.	Ch. 3.1-3.3	301-311.
15/4	Sampling. Aliasing.	Ch. 3.4-3.5	312-321.
17/4	Gaussian processes. Filtering.	Ch. 4.1-4.3, 5.1-5.5	401-409.
22/4	Filtering.	Ch. 5.1-5.5	501-508.
24/4	Linear filters.	Ch. 6.1-6.3	509-515.
29/4	Linear filters.	Ch. 6.1-6.3	601-611.
6/5	Linear filters. Continuous time.	Ch. 6.1-6.3, 7.1-7.3	612-620.
13/5	Optimal filtering.	Ch. 7.1-7.4	701-708.
15/5	Spectral estimation.	Ch. 8.1-8.4	801-809.
20/5	Repetition.		Repetition.
22/5	Reserve.

Computer exercises

The course contains three mandatory computer exercises. You need to sign up for all three exercises; write your name on the lists which are posted on the bulletin board at the ground floor of the mathematical department. The Matlab files required to do the exercises can be downloaded here.

• Exercise 1
• 17/4, 10-12, MH:230
• 18/4, 13-15, MH:230

• Exercise 2
• 29/4, 10-12, MH:230
• 02/5, 13-15, MH:230

• Exercise 3
• 16/5, 08-10, MH:230
• 16/5, 15-17, MH:230

Suitable further courses

• FMS 047 Stationary Stochastic Processes, Project.
• FMS 110/MAS 222 Time Series Analysis.
• FMS 161/MAS 229 Markov processes.

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