Description:

The course is devoted in part to the basic notions of the general theory of random processes and partially to the theory of stationary processes and sequences both weakly and strongly stationary ones.

Contents:

Notion of a random peocess, Kolmogorovˇs theorem, properties of trajectories, elements of stochastic analysis, random derivative and random integral, Wiener process, Karhunen´s theorem and spectral resolution of a random process, weak stationarity, spectral density and a linear process, ergodic theorem for weakly stationary processes, question of prediction for weakly stationary processes andsequences, strong stationarity, ergodic theorems for strongly stationary processes.

Recommended literature:

Key references:
M.B. Priestley: Spectral Analysis and Time Series, Academic Press, 1981

Recommended references:
P.Z.Peebles: Probabilty, Random Variables and Random Signal Principles, McGraw-Hill , 2001

Keywords:

random process and random sequence, staochastic analzsis and random integral, spectral resolution, weak and strong stationarity, prediction, ergodic theorems.

Abbreviations used:

Semester:

• W ... winter semester (usually October - February)
• S ... spring semester (usually March - June)
• W,S ... both semesters

Mode of completion of the course:

• A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
• GA ... Graded Assessment (a grade is awarded for this course)
• EX ... Examination (a grade is awarded for this course)
• A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)

Weekly load (hours per week):

• P ... lecture
• C ... seminar
• L ... laboratory
• R ... proseminar
• S ... seminar