â€” Pure and applied mathematics

â€” Engineering

â€” Economics

â€” Finance

and other related fields.

The present course introduces the main concepts of the theory of stochastic processes and its applications. During the study, the students will get acquainted with various types of stochastic processes and learn to analyse their basic properties and characteristics. The material is anticipated to be of great interest for students willing to enhance their knowledge of stochastics and its use for the analysis of complex dynamical systems arising in various fields, such as economics or engineering.

The main purpose of this course is to introduce the main concepts of the theory of stochastic processes and provide some ideas for its application to the solution of various problems in economics, finance, and other related fields.

The course relies on the basic knowledge in the following disciplines:

â€” probability theory (e.g., discrete and continuous distributions, conditional probability, calculation of moments, covariance, basic characteristics of functions of random variables)

â€” calculus (e.g., integration, double integration, differentiation, trigonometry)

â€” linear algebra (solution of systems of linear equations)

Acquaintance with the basics of mathematical statistics is not required but simplifies the understanding of this course.

Each week is followed by a test containing both theoretical and practical problems related to the covered material. At the end of the course the students are encouraged to complete the final exam, which comprises various problems on all the topics discussed during the lectures.

No specific software is needed for the completion of this course.

The course provides a solid theoretical basis for studying further disciplines in stochastics, such as stochastic modelling and financial mathematics. In addition, the reading materials contain the examples of real-life applications of the studied concepts, which might be helpful for designing the own solutions for various problems arising in scientific research, business and other areas.

The course consists of short video lectures, up to 20 minutes long, some of which contain non-graded questions which enhance the understanding of the material. Each week there is a test with an estimated completion time of 1 hour. The final exam consists of test problems covering all the material and is expected to take approximately 1.5 hours to complete.