Опис навчальної дисципліни

The purpose of teaching the course is to master students’ basic theoretical information and practical skills of the course. The program provides students with random processes with: continuous states and continuous and discrete time, and discrete states and discrete and continuous time (Markov chains and Markov processes).

To teach students to use the apparatus of random processes for formalization and mathematical modeling of applied problems for their effective software and hardware implementation. Considerable attention will be paid to the use of Markov processes for description, Markov-type queuing systems.

Learning outcomes:

The student must know:

– basic concepts of the theory of random processes: definition and classification of random processes;
distribution laws and basic characteristics of random processes;
vector and complex random processes;
transformation of random processes and operations on them;
stationary and ergodic random processes;
correlation analysis;
spectral description of random processes;
event flows, their properties and classification.
Markov chains and Markov processes with discrete states and continuous time;
basics of queuing theory.

The student must be able to:

calculate the basic characteristics of random processes according to the given laws of probability distribution;
describe linear transformations of random processes in the black box model;
analyze the processes of stationarity and ergodicity;
describe the processes in the spectral domain;
apply Markov chains and Markov processes with discrete states and continuous time to solve practical problems;
apply the concepts and relations of queuing theory to the analysis of problems.