| 1. | Course Title | Stochastic Differential Equations | |||||||||||
| 2. | Code | 4ФЕИТ08024 | |||||||||||
| 3. | Study program | 13-PMA, 16-MNT | |||||||||||
| 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 Biljana Jolevska-Tuneska | |||||||||||
| 9. | Course Prerequisites | ||||||||||||
| 10. | Course Goals (acquired competencies):
The student is introduced to stochastic processes and Ito integrals. The student knows how to solve simple stochastic differential equations and discusses the type of solution (weak or strong). The student knows how to recognize linear stochastic differential equations and vector stochastic differential equations. |
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| 11. | Course Syllabus:
Introduction to stochastic processes. Mathematical interpretation of equations involving noise. Martingales. Ito processes (stochastic integrals). One-dimensional and multi-dimensional Ito’s formula. Existence and uniqueness theorem of stochastic differential equations. Weak and strong solutions. A linear stochastic differential equation. Reducible stochastic differential equations. Some equations are solved explicitly. Vector stochastic differential equations. |
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| 12. | Learning methods:
Blended way of learning: lectures supported by presentations and visualization of concepts and independent project assignments. |
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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 | 20 points | |||||||||||
| 17.4. | Final exam | 30 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 | none | |||||||||||
| 20. | Forms of assessment | Project assignment and final exam | |||||||||||
| 21. | Language | Macedonian and English | |||||||||||
| 22. | Method of monitoring of teaching quality | Self evaluation | |||||||||||
| 23. | Literature | ||||||||||||
| 23.1. | Required Literature | ||||||||||||
| No. | Author | Title | Publisher | Year | |||||||||
| 1. | B. Oksendal | Stochastic Differential Equations: An introduction with Applications, fourth edition | Springer-Verlag | 1996 | |||||||||
| 23.2. | Additional Literature | ||||||||||||
| No. | Author | Title | Publisher | Year | |||||||||
| 1. | A. Friedman | Stochastic Differential Equations and Applications | Dover books of mathematics | 2006 | |||||||||
