2021 Advanced topics in Analysis G

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Academic unit or major
Graduate major in Mathematics
Ninomiya Syoiti 
Course component(s)
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Syllabus updated
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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.


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)

Out-of-Class Study Time (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.


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


None in particular
Information about this lecture will be announced via T2SCHOLA.

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