| 1. | Course Title | Numerical Methods in Stochastic Processes | |||||||||||
| 2. | Code | 4ФЕИТ08015 | |||||||||||
| 3. | Study program | 13-PMA | |||||||||||
| 4. | Organizer of the study program (unit, institute, department) | Faculty of Electrical Engineering and Information Technologies | |||||||||||
| 5. | Degree (first, second, third cycle) | Second cycle | |||||||||||
| 6. | Academic year/semester | I/1 | 7. | Number of ECTS credits | 6.00 | ||||||||
| 8. | Lecturer | Dr Sonja Gegovska-Zajkova | |||||||||||
| 9. | Course Prerequisites | ||||||||||||
| 10. | Course Goals (acquired competencies):
After completing this course, student should be able to analyze the convergence and the stability properties of stochastic numerical methods, to implement numerical methods for solving stochastic differential equations, to identify and understand the mathematical modeling of stochastic processes, and choose an appropriate numerical method to solve stochastic differential equations. |
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| 11. | Course Syllabus:
Strong numerical approximations for stochastic differential equations: Galerkin approximations, Euler–Maruyama and Milstein approximations. Noise approximations. Week approximation. Mild-Ito formula. Stochastic simulations and multi-level Monte-Carlo methods. |
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| 12. | Learning methods:
A blended learning method consisting of traditional classroom methods, independent study and e-learning. |
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| 13. | Total number of course hours | 180 | |||||||||||
| 14. | Distribution of course hours | 3 + 3 | |||||||||||
| 15. | Forms of teaching | 15.1 | Lectures-theoretical teaching | 45 hours | |||||||||
| 15.2 | Exercises (laboratory, practice classes), seminars, teamwork | 45 hours | |||||||||||
| 16. | Other course activities | 16.1 | Projects, seminar papers | 30 hours | |||||||||
| 16.2 | Individual tasks | 30 hours | |||||||||||
| 16.3 | Homework and self-learning | 30 hours | |||||||||||
| 17. | Grading | ||||||||||||
| 17.1 | Exams | 0 points | |||||||||||
| 17.2 | Seminar work/project (presentation: written and oral) | 50 points | |||||||||||
| 17.3. | Activity and participation | 0 points | |||||||||||
| 17.4. | Final exam | 50 points | |||||||||||
| 18. | Grading criteria (points) | up to 50 points | 5 (five) (F) | ||||||||||
| from 51 to 60 points | 6 (six) (E) | ||||||||||||
| from 61 to 70 points | 7 (seven) (D) | ||||||||||||
| from 71 to 80 points | 8 (eight) (C) | ||||||||||||
| from 81 to 90 points | 9 (nine) (B) | ||||||||||||
| from 91 to 100 points | 10 (ten) (A) | ||||||||||||
| 19. | Conditions for acquiring teacher’s signature and for taking final exam | 60% success of all activities | |||||||||||
| 20. | Forms of assessment | Preparation and presentation of a project assignment | |||||||||||
| 21. | Language | Macedonian and English | |||||||||||
| 22. | Method of monitoring of teaching quality | Selfevaluation | |||||||||||
| 23. | Literature | ||||||||||||
| 23.1. | Required Literature | ||||||||||||
| No. | Author | Title | Publisher | Year | |||||||||
| 1. | Raúl Toral, Pere Colet | Stochastic Numerical Methods: An Introduction for Students and Scientists | John Wiley & Sons-VCH | 2014 | |||||||||
| 2. | D. J. HighamP.E. Kloeden | An Introduction to the Numerical Simulation of Stochastic Differential Equations | SIAM – Society for Industrial and Applied Mathematics | 2021 | |||||||||
