2025 (Current Year) Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Advanced topics in Analysis H
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Hideki Tanemura
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 3-4 Thu
- Class
- -
- Course Code
- MTH.C504
- Number of credits
- 100
- Course offered
- 2025
- Offered quarter
- 2Q
- Syllabus updated
- Apr 2, 2025
- Language
- English
Syllabus
Course overview and goals
In this lecture, the topics discussed in ``Advanced topics in analysis G'' are developed in continuous time models.
The following notions such as Ito integral, Stochastic Differential Equations, and some models in mathematical finance are discussed.
Course description and aims
Understanding the following notions:
Ito calculus and basic knowledge of stochastic differential equations
Keywords
Ito calculus, 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 | Ito integral (stochastic integral)(1), definition | Details will be provided each class session. |
| Class 2 | Ito integral (2), basic properties | |
| Class 3 | Ito formula | |
| Class 4 | Ito Representation theorem | |
| Class 5 | Stochastic Differential Equation (1), Existence of the solution | |
| Class 6 | Stochastic Differential Equation (2), Approximations of solutions | |
| Class 7 | Stochastic Differential Equation (3) | |
| Class 8 | Mathematical Finance |
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
Kusuoka, S., ``Stochastic Analysis,'' Chisenshokan
Evaluation methods and criteria
Based on reports. Details will be provided in the class.
Related courses
- MTH.C361 ： Probability Theory
- MTH.C503 ： Advanced topics in Analysis G
Prerequisites
None in particular
Other
None in particular
Information about this lecture will be announced via T2SCHOLA.