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Level: Master Semestre: 1st ECTS: 5 Working Hours:
- Contact: 32
- Seminars: 16
- Self-study: 132
- Total: 180
Language of Instruction: English (Russian) Author of the Course: Serguei Pergamenchtchikov, Doctor of Science, Professor Lecturers: Serguei Pergamenchtchikov, Doctor of Science, Professor
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Objectives:
- Studying of the modern stochastic calculus and its application to the modeling of stochastic dynamical systems described by stochastic differential and stochastic difference equations;
- Application of the theory of measurable maps, measure theory and methods of analytic functions for the development of the basic concepts of the modern theory stochastic processes such as:
Conditional expectations and their applications in the theory of stochastic processes;
Stochastic basis and basic measurable structure;
Markov moments;
Random sets;
Random processes;
Martingales;
Stochastic integration.
Learning Outcomes:
To know: the basic principles of modern stochastic calculus;
To be able: to properly use the stochastic integration methods, perform correct limit transitions in the localization methods of stochastic processes by the stopping times;
To have: the skills to the limiting transitions under the sign of conditional expectations, the stopping times tool, the stochastic integration methods.
Assessment Methods:
The current control of mastering the discipline includes two written test.
The final control – exam.
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