Objectives and outcomes
Students are able to think abstractly and acquire knowledge about random processes. They analyse
a theory that describes the behaviour of random signals and processes in the real world. Students are
able to use the acquired knowledge in the field of random processes in further education and scientific
research.
Lectures
Introduction to probability: axioms, equally likely experimental results, geometric probability.
Conditional probability, independence. Bayes’ formula and its consequences. The notion of random
variables and random vectors. Numerical characteristics. Conditional expectation. Approximate
determination of a random variable. Characteristic functions. Law of large numbers and the central limit
theorem. Discrete-time random processes. Stochastic input systems. Degree spectrum. Random
movement. Wiener processes. Deterministic signals in noise. System identification.
Fourier series and extensions of Karhunen-Loeve. Spectral representation of random
processes. Approximate determination using mean squares. Filtering and prediction. Kalman filter. The
concept of entropy. Maximum entropy method. Markov chains. Chapman-Kolmogorov equations.
Condition classification. Branching processes. Introduction to queuing theory.
Research work
Research work includes active monitoring of primary scientific sources, organisation and performance of
experiments and statistical data processing, numerical simulations and writing a scientific paper.
.