Stationary Stochastic Processes

News

• Office hour for last minute questions on Wednesday 23/5, at 9-10, in MH:225.
• There will be an additional possibility to pass the computer exercises on Tuesday 15th, at 8-10, in MH:230. This is not a regular computer exercise, only an opportunity for you to pass the exercises if you have missed any of them before. You should come well prepared.
• Note that the exercise on Wednesdays are at 8-10. See here for further details on the schedule.

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 KF Sigma. The problem booklet and the table of formulas can be downloaded here and here. You might also find the following study questions useful. The course program is available here.
Schedule: The course start on Monday, March 12th, at 13.15, in M:B. Lectures are Mondays and Wednesdays at 13-15, in M:B (although note the two exceptions!). Tutorials are offered on Tuesdays 10-12 and 13-15, Wednesdays 8-10, and Fridays 10-12, 13-15, and 15-17. You are welcome to attend any and as many of these sessions as you prefer. You can find the detailed schedule here.
Exam: The final exam is held on May 24th, at 8-13, in Vic:3A/3B/3C. The retake exam will be held on August 25th, at 8-13. A collection of old exams can be found here. On the exam, you are allowed to bring a pocket calculator, the table of formulas for this and for the basic course, as well as a standard table of formulas.

People

Lecturer:
Andreas Jakobsson
Tutorials:
Oskar Arnström
John Hedestig
Simon Johansson
Computer exercises:
Oskar Arnström
Filip Erntell
John Hedestig
Elham Pirnia
Course secretary:
Maria Lövgren

Preliminary schedule

Date	Lecture	Reading instructions	Problems
12/3	Introduction and overview.	Ch 1.1-1.4, 2.1-2.5	201-208.
14/3	Moment functions. Stationarity.	Ch. 2.1-2.5	209-214.
19/3	Ergodicity. Estimation.	Ch. 2.1-2.5	215-221.
21/3	Spectral representation.	Ch. 3.1-3.3	301-311.
26/3	Sampling. Aliasing.	Ch. 3.4-3.5	312-321.
28/3	Gaussian processes. Filtering.	Ch. 4.1-4.3, 5.1-5.5	401-409.
17/4	Filtering.	Ch. 5.1-5.5	501-508.
18/4	Linear filters.	Ch. 6.1-6.3	509-515.
23/4	Linear filters.	Ch. 6.1-6.3	601-611.
25/4	Linear filters. Continuous time.	Ch. 6.1-6.3, 7.1-7.3	612-620.
2/5	Optimal filtering.	Ch. 7.1-7.4	701-708.
7/5	Spectral estimation.	Ch. 8.1-8.4	801-809.
9/5	Repetition.		Repetition.
14/5	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
• 27/3, 8-10, MH:230
• 28/3, 15-17, MH:230
• 28/3, 17-19, MH:230
• 29/3, 8-10, MH:230

• Exercise 2
• 24/4, 8-10, MH:230
• 25/4, 15-17, MH:230
• 25/4, 17-19, MH:230
• 26/4, 8-10, MH:230

• Exercise 3
• 8/5, 8-10, MH:230
• 9/5, 10-12, MH:230
• 9/5, 17-19, MH:230
• 10/5, 8-10, 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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