Hiroshima University Syllabus

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Academic Year 2022Year School/Graduate School School of Informatics and Data Science
Lecture Code KA224001 Subject Classification Specialized Education
Subject Name 確率過程論
Subject Name
Subject Name in
Stochastic Processes
シマ タダシ
Campus Higashi-Hiroshima Semester/Term 3rd-Year,  Second Semester,  4Term
Days, Periods, and Classrooms (4T) Tues5-6,Thur5-6:IAS K209
Lesson Style Lecture Lesson Style
(More Details)
My teaching style in this class is heavily depend on a blackboard. 
Credits 2.0 Class Hours/Week   Language of Instruction B : Japanese/English
Course Level 3 : Undergraduate High-Intermediate
Course Area(Area) 25 : Science and Technology
Course Area(Discipline) 01 : Mathematics/Statistics
Eligible Students
Keywords measure theory, probability, stochastic processes, Brownian motion 
Special Subject for Teacher Education   Special Subject  
Class Status
within Educational
Criterion referenced
Informatics and Data Science Program
(Comprehensive Abilities)
・D3. Ability to examine social needs and issues which are interlinked in a complex manner, using a top-down view to solve the problems through quantitative and logical thinking based on data, diverse perspectives, and advanced skills in information processing and analysis.
Class Objectives
/Class Outline
"Stochastic processes" is a mathematical concept to describe time development
of random phenomena, such as the fluctuation of stock prices or the length of a queue for a cash dispenser.
The aims of this course are to introduce students to measure theoretic probability
and basic concepts of the theory of stochastic processes
and to develop their problem-solving skills.
Class Schedule In my plan, the contents of this course are divided into 3 chapters as follows:
I. Measure theory,
II. The basic concepts of probability,
III. Stochastic processes.
On the 1st chapter, We discuss the measure theory, especially topics which are relevant to
the next chapter. The goal for this chapter is Radon-Nykodym theorem. On the next chapter,
we try to clarify the concepts of probability by using the measure theory.
Conditional probabilities and conditional expectations are defined rigorously.
On the final part, we introduce the basic concepts of stochastic processes and Brownian motion. We will then discuss the strong Markov property and the theory of martingale which are important properties of Brownian motion.

実解析入門,猪狩 惺,岩波書店
ルベーグ積分入門,吉田 伸生,星雲社
ルベーグ積分, 岩田 耕一郎,森北出版
A User's Guide to Measure Theoretic Probability
確率論, 伊藤 清, 岩波書店
測度と確率1,2, 小谷 真一, 岩波講座 現代数学の基礎
確率過程入門, 西尾眞喜子, 樋口保成, 培風館

PC or AV used in
(More Details) the textbook will be indicated in the class. 
Learning techniques to be incorporated  
Suggestions on
Preparation and
In each class, I submit some problems as exercises.
So, review and try to solve them. 
Requirements The prerequisites for this course are Calculus and introductory probability theory.

Grading Method Students will be graded based on their report.  
Practical Experience  
Summary of Practical Experience and Class Contents based on it  
Please fill in the class improvement questionnaire which is carried out on all classes.
Instructors will reflect on your feedback and utilize the information for improving their teaching. 
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