Facts
Duration: 1 semester
Period: Fall Semester
Credits: 6 ECTS
Contact Hours: 64
Self-study: 152
Hours: 216
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Main Objectives
1. The studying of the modern stochastic calculus and its application to the modeling of stochastic dynamical systems described by stochastic differential and stochastic difference equations.
2. 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;
- andom processes;
- martingales;
- Stochastic integration.
Learning Outcomes
In mastering the subject the student will acquire the following knowledge:
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 o fconditional expectations, the stopping times tool, the stochastic integration methods.
Professor
Serguei Pergamenchtchikov, Doctor of Science
Course unit code |
Б.2.2 |
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Course unit title |
Basic course |
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Name(s), surname(s) and title of lecturer(s) |
Serguei Pergamenchtchikov, Doctor of Science, Professor |
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Semester |
1 |
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ECTS credits |
6 |
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Working hours |
Contact hours |
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lectures |
32 |
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seminars |
32 |
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Self-study |
152 |
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Total |
216 |
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Work placement |
Laboratory works in Computer class |
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Prerequisites |
To study the course one needs «Topology", "Mathematical Analysis", "Functional Analysis", "Theory of functions of a complex variable" and "Theory of Probability and Mathematical Statistics". |
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Language of instruction |
English (Russian) |
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Objectives of the course |
Learning outcomes |
A student’s assessments methods |
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1.1. The studying of the modern stochastic calculus and its application to the modeling of stochastic dynamical systems described by stochastic differential and stochastic difference equations. 1.2. 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. |
In mastering the subject the student will acquire the following knowledge: 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. |
The current control of mastering the discipline includes two written test. The final control – exam. |
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Teaching methods |
Lectures, Labs |
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List of Topics |
Topic title |
Contact hours |
Assignments and independent study hours |
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Conditional expectations |
8 |
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Stopping times |
8 |
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Random sets |
8 |
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Random processes |
10 |
Written test 1 |
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Optional and predictable processes |
8 |
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Martingales |
10 |
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Stochastic integral |
12 |
Written test 2 |
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64 |
Exam |
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Assessment requirements |
In during the semester 40 points |
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Assessment criteria |
Each test 20 points |
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The composition of final accumulative mark |
Exam 60 points. Examination ticket consists of two theoretical questions (10x2=20) and two exercises (20x2=40). |
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Author of the course |
Serguei Pergamenchtchikov |