2024 Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Advanced topics in Analysis G
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Syoiti Ninomiya
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 3-4 Thu
- Class
- -
- Course Code
- MTH.C503
- Number of credits
- 100
- Course offered
- 2024
- Offered quarter
- 1Q
- Syllabus updated
- Mar 14, 2025
- Language
- English
Syllabus
Course overview and goals
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.
Course description and aims
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
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
Blackboard and handouts
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| 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) |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
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)
Evaluation methods and criteria
Based on reports. Details will be provided in the class.
Related courses
- MTH.C361 ： Probability Theory
- MTH.C504 ： Advanced topics in Analysis H
Prerequisites
None in particular
Other
None in particular
Information about this lecture will be announced via T2SCHOLA.