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.
Understanding the notions of martingales in continuous time setting, Brownian motion, Ito integral, and stochastic differential equations.
Martingale, Browinian motion, Ito integral, Stochastic Differential Equation, Mathematical Finance
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Blackboard and handouts
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) |
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.
None in particular.
Taniguchi, S., ``Stochastic Differential Equations,'' Kyoritsu (in Japanese)
Kusuoka, S., ``Stochastic Analysis,'' Chisenshokan (in Japanese)
Based on reports. Details will be provided in the class.
None in particular
None in particular