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- Common courses
- Liberal arts and basic science courses
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Ninomiya Syoiti
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Thr3-4(H137)
- Group
- -
- Course number
- MTH.C503
- Credits
- 1
- Academic year
- 2019
- Offered quarter
- 1Q
- Syllabus updated
- 2019/3/18
- Lecture notes updated
- 2019/4/4
- Language used
- English
- Access Index
-
Course description and aims
This lecture and its sequel ``Advanced topics in analysis H'' are aimed at those wishing to learn about Ito integral (stochastic integral) and stochastic differential equations.
Student learning outcomes
Understanding the notions of martingales in continuous time setting, Brownian motion, Ito integral, and stochastic differential equations.
Keywords
Martingale, Browinian motion, Ito integral, Stochastic Differential Equation, Mathematical Finance
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
Blackboard and handouts
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Probability Theory | Details will be provided each class session. |
| Class 2 | Stochastic Process | |
| Class 3 | Martingale(1), definition | |
| Class 4 | Martingale(2), Optional Sampling Theorem | |
| Class 5 | Quadratic Variational Process | |
| Class 6 | Brownian motion(1) definition, existence | |
| Class 7 | Brownian motion (2): important properties | |
| Class 8 | Ito Integral (Stochastic Integral) |
Textbook(s)
None in particular.
Reference books, course materials, etc.
Taniguchi, S., ``Stochastic Differential Equations,'' Kyoritsu (in Japanese)
Kusuoka, S., ``Stochastic Analysis,'' Chisenshokan (in Japanese)
Assessment criteria and methods
Based on reports. Details will be provided in the class.
Related courses
- MTH.C361 ： Probability Theory
- MTH.C504 ： Advanced topics in Analysis H
Prerequisites (i.e., required knowledge, skills, courses, etc.)
None in particular
Other
None in particular
