Theory of Random Processes

Garant předmětu:

Jan Vybíral

Lecturer:

Jan Vybíral

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

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.

Requirements:

Basic course of Calculus and Linear Algebra, Course of Probability Theory and Mathematical Statistics

Syllabus of lectures:

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.

Syllabus of tutorials:

Study Objective:

Basic elements of rheora of random processes, notion of a random integral, theory of weakly stationary and strongly stationary processes. Skills: Mainly application of theory of weakly stationary processes in ingineering practice.

Study materials:

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

Note:

Time-table for winter semester 2023/2024:

Time-table is not available yet

Time-table for summer semester 2023/2024:

Time-table is not available yet

The course is a part of the following study plans:

• Matematické inženýrství (compulsory course of the specialization)
• Aplikace softwarového inženýrství (elective course)
• Aplikovaná algebra a analýza (compulsory course in the program)
• Aplikované matematicko-stochastické metody (compulsory course in the program)
• Matematická fyzika (elective course)
• Matematické inženýrství (compulsory course in the program)