KA224001 Stochastic Processes

Hiroshima University Syllabus

Japanese

Academic Year 2024Year 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
（Katakana）カクリツカテイロン

Subject Name in
English Stochastic Processes

Instructor SHIMA TADASHI

Instructor
(Katakana) シマ　タダシ

Campus Higashi-Hiroshima Semester/Term 3rd-Year,  Second Semester,  4Term

Days, Periods, and Classrooms (4T) Tues5-6：IAS K204, (4T) Thur5-6：IAS K208

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
Program
(Applicable only to targeted subjects for undergraduate students)
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students) Computer Science Program
（Abilities and Skills）
・A. Information infrastructure development technology, information processing technology, technology that analyzes data and creates new added value.

Data Science Program
（Comprehensive Abilities）
・D3. Ability to overlook social needs and issues that are intertwined in a complex manner and to solve issues with quantitative and logical thinking based on data, a multifaceted perspective, and advanced information analysis ability.

Intelligence Science Program
（Comprehensive Abilities）
・D3. Ability to grasp complexly intertwined social needs and issues from a bird's-eye view and solve issues with a multifaceted perspective and analytical ability based on a wide range of knowledge in intelligent science.

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 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.

Text/Reference
Books,etc. 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
確率論，舟木直久，朝倉書店
確率論,  岩田耕一郎, 森北出版

PC or AV used in
Class,etc. 　

(More Details) the textbook will be indicated in the class.

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review 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

Message

Other

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.

Academic Year	2024Year	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 （Katakana）	カクリツカテイロン
Subject Name in English	Stochastic Processes
Instructor	SHIMA TADASHI
Instructor (Katakana)	シマ　タダシ
Campus	Higashi-Hiroshima	Semester/Term	3rd-Year, Second Semester, 4Term
Days, Periods, and Classrooms	(4T) Tues5-6：IAS K204, (4T) Thur5-6：IAS K208
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 Program (Applicable only to targeted subjects for undergraduate students)
Criterion referenced Evaluation (Applicable only to targeted subjects for undergraduate students)	Computer Science Program （Abilities and Skills）・A. Information infrastructure development technology, information processing technology, technology that analyzes data and creates new added value. Data Science Program （Comprehensive Abilities）・D3. Ability to overlook social needs and issues that are intertwined in a complex manner and to solve issues with quantitative and logical thinking based on data, a multifaceted perspective, and advanced information analysis ability. Intelligence Science Program （Comprehensive Abilities）・D3. Ability to grasp complexly intertwined social needs and issues from a bird's-eye view and solve issues with a multifaceted perspective and analytical ability based on a wide range of knowledge in intelligent science.
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 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.
Text/Reference Books,etc.	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, 培風館確率論，舟木直久，朝倉書店確率論, 岩田耕一郎, 森北出版
PC or AV used in Class,etc.
(More Details)	the textbook will be indicated in the class.
Learning techniques to be incorporated
Suggestions on Preparation and Review	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
Message
Other
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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