Course title
6M0097001
Stochastic Calculus

 NAKATSU Tomonori
Course content
Lectures on Stochastic calculus
Purpose of class
Learn Stochastic calculus
Goals and objectives
  1. Learn stochastic integral with respect to martingale theory.
  2. Understand the proof and application of Ito's formula.
  3. Construct a solution to stochastic differential equations.
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 レポート Total.
1. 100% 100%
Total. 100% -
Language
Japanese
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1． Brownian motion: definition and properties Review of lectures 180minutes
2． Martingale Review of lectures 180minutes
3． Martingale Review of lectures 180minutes
4． Quadratic variation Review of lectures 180minutes
5． Quadratic variation Review of lectures 180minutes
6． Quadratic variation Review of lectures 180minutes
7． Definition of stochastic integral Review of lectures 180minutes
8． Properties of stochastic integral Review of lectures 180minutes
9． Ito's formula Review of lectures 180minutes
10． Ito's formula Review of lectures 180minutes
11． Ito's formula Review of lectures 180minutes
12． Stochastic differential equation: existence and uniqueness of solution Review of lectures 180minutes
13． Stochastic differential equation: existence and uniqueness of solution Review of lectures 180minutes
14． Stochastic differential equation: estimates of solution Review of lectures 180minutes
Total. - - 2520minutes
Evaluation method and criteria
Report
Feedback on exams, assignments, etc.
ways of feedback specific contents about "Other"
Feedback in outside of the class (ScombZ, mail, etc.)
Textbooks and reference materials
The following would be helpful:
「確率微分方程式」長井英生著、共立出版
Prerequisites
Review measure theory and probability theory
Office hours and How to contact professors for questions
  • e-mail
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Course that cultivates an ability for utilizing knowledge
Active-learning course
More than one class is interactive
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicable
Applicable Nakatsu worked at a financial institute for 4 years.
Education related SDGs:the Sustainable Development Goals
  • 4.QUALITY EDUCATION
  • 8.DECENT WORK AND ECONOMIC GROWTH
Last modified : Thu Feb 27 10:50:26 JST 2025