ANM19001 Theory of Stochastic Processes

Hiroshima University Syllabus

Japanese

Academic Year 2024Year School/Graduate School School of Integrated Arts and Sciences Department of Integrated Arts and Sciences

Lecture Code ANM19001 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 Theory of Stochastic Processes

Instructor KODAMA MEI

Instructor
(Katakana) コダマ　メイ

Campus Higashi-Hiroshima Semester/Term 3rd-Year,  First Semester,  2Term

Days, Periods, and Classrooms (2T) Thur5-8：IAS C808

Lesson Style Lecture Lesson Style
(More Details) 　

My teaching style in this class is heavily depend on a blackboard.
/ Online

Credits 2.0 Class Hours/Week 　 Language of Instruction J : Japanese

Course Level 3 : Undergraduate High-Intermediate

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 01 : Mathematics/Statistics

Eligible Students Third/ Fourth Grade students in Faculty of Integrated Arts and Sciences, and other students

Keywords probability, stochastic process

Special Subject for Teacher Education 　 Special Subject 　

Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students) Explain fundamentals of stochastic process theory with models and expressions for information.
This provides a part of foundations of science based on probability and stochastic process.
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students) Integrated Arts and Sciences
（Knowledge and Understanding）
・Knowledge and understanding of the importance and characteristics of each discipline and basic theoretical framework.
・The knowledge and understanding  to fully recognize the mutual relations and their importance among individual academic diciplines.
（Abilities and Skills）
・The ability and skills to specify necessary theories and methods for consideration of issues.

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 aim of this course is to introduce students to some basic concepts regarding the theory of stochastic processes and to develop their problem-solving skills.

Class Schedule lesson 1: guidance, foundation of probability #1
lesson 2:  foundation of probability #2
lesson 3: probability space, random variable
lesson 4: analytical theory of probabiity distribution
lesson 5: independency and dependency of random variables
lesson 6: foundation of the limit theorem
lesson 7: random walk
lesson 8: Markov chain #1
lesson 9: Markov chain #2
lesson 10: counting process
lesson 11: continuous-time Markov chains #1
lesson 12: continuous-time Markov chains #2
lesson 13: queuing sysem #1
lesson 14: queuing sysem #2
lesson 15: queuing sysem #3, conclusion

report, mini examination, final examination / report (online)

Text/Reference
Books,etc. 確率論, 大平徹, 森北出版
確率過程の基礎, R.デュレット, 丸善出版
確率モデル要論, 尾畑伸明, 牧野書店
わかりやすい待ち行列システム-理論と実践-, 高橋，山本，吉野，戸田，電子情報通信学会

PC or AV used in
Class,etc. 　

(More Details) Handouts, projector, online

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review The materials will be used in Moodle system.
No.1: guidance and basics of probability #1 will be reviewed.
No.2: the basics of probability #2 will be reviewed.
No.3: the basic properties of probability space, random variables, and
the basics of stochastic processes will be explained.
No.4: one-dimensional distribution, discrete distribution, continuous
distribution, density function, etc. will be explained.
No.5: independence and conditional probabilities of events, independent random variables, etc. will be explained.
No.6: the convergence of random variable sequences, the law of large
numbers, and the central limit theorem will be explained.
No.7: one-dimensional random walk, Catalan number, recursion, etc. will be explained.
No.8,9: the state space, transition probabilities, recursiveness,
number of arrivals, stationary distribution, and Markov chains will be
explained.
No.10: birth and death process, Poisson process will be explained.
No.11,12: the definition of continuous-time Markov chains, transition
probabilities, limit behavior, queuing theory, renewal theory, etc. will be explained.
No.13-15: The basics of the queuing system (M/M/1 system, M/M/1/K system, etc.) will be explained. Finally, we summarize this lecture.

Requirements The prerequisites for this class are Calculus and Linear Algebra.
Familiarity with infinite series is desirable.

Grading Method Students will be graded based on their report 20%, mini exam 20% and final exam 60% (or reports).

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 Integrated Arts and Sciences Department of Integrated Arts and Sciences
Lecture Code	ANM19001	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	Theory of Stochastic Processes
Instructor	KODAMA MEI
Instructor (Katakana)	コダマ　メイ
Campus	Higashi-Hiroshima	Semester/Term	3rd-Year, First Semester, 2Term
Days, Periods, and Classrooms	(2T) Thur5-8：IAS C808
Lesson Style	Lecture	Lesson Style (More Details)
My teaching style in this class is heavily depend on a blackboard. / Online
Credits	2.0	Class Hours/Week		Language of Instruction	J : Japanese
Course Level	3 : Undergraduate High-Intermediate
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	01 : Mathematics/Statistics
Eligible Students	Third/ Fourth Grade students in Faculty of Integrated Arts and Sciences, and other students
Keywords	probability, stochastic process
Special Subject for Teacher Education		Special Subject
Class Status within Educational Program (Applicable only to targeted subjects for undergraduate students)	Explain fundamentals of stochastic process theory with models and expressions for information. This provides a part of foundations of science based on probability and stochastic process.
Criterion referenced Evaluation (Applicable only to targeted subjects for undergraduate students)	Integrated Arts and Sciences （Knowledge and Understanding）・Knowledge and understanding of the importance and characteristics of each discipline and basic theoretical framework. ・The knowledge and understanding to fully recognize the mutual relations and their importance among individual academic diciplines. （Abilities and Skills）・The ability and skills to specify necessary theories and methods for consideration of issues.
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 aim of this course is to introduce students to some basic concepts regarding the theory of stochastic processes and to develop their problem-solving skills.
Class Schedule	lesson 1: guidance, foundation of probability #1 lesson 2: foundation of probability #2 lesson 3: probability space, random variable lesson 4: analytical theory of probabiity distribution lesson 5: independency and dependency of random variables lesson 6: foundation of the limit theorem lesson 7: random walk lesson 8: Markov chain #1 lesson 9: Markov chain #2 lesson 10: counting process lesson 11: continuous-time Markov chains #1 lesson 12: continuous-time Markov chains #2 lesson 13: queuing sysem #1 lesson 14: queuing sysem #2 lesson 15: queuing sysem #3, conclusion report, mini examination, final examination / report (online)
Text/Reference Books,etc.	確率論, 大平徹, 森北出版確率過程の基礎, R.デュレット, 丸善出版確率モデル要論, 尾畑伸明, 牧野書店わかりやすい待ち行列システム-理論と実践-, 高橋，山本，吉野，戸田，電子情報通信学会
PC or AV used in Class,etc.
(More Details)	Handouts, projector, online
Learning techniques to be incorporated
Suggestions on Preparation and Review	The materials will be used in Moodle system. No.1: guidance and basics of probability #1 will be reviewed. No.2: the basics of probability #2 will be reviewed. No.3: the basic properties of probability space, random variables, and the basics of stochastic processes will be explained. No.4: one-dimensional distribution, discrete distribution, continuous distribution, density function, etc. will be explained. No.5: independence and conditional probabilities of events, independent random variables, etc. will be explained. No.6: the convergence of random variable sequences, the law of large numbers, and the central limit theorem will be explained. No.7: one-dimensional random walk, Catalan number, recursion, etc. will be explained. No.8,9: the state space, transition probabilities, recursiveness, number of arrivals, stationary distribution, and Markov chains will be explained. No.10: birth and death process, Poisson process will be explained. No.11,12: the definition of continuous-time Markov chains, transition probabilities, limit behavior, queuing theory, renewal theory, etc. will be explained. No.13-15: The basics of the queuing system (M/M/1 system, M/M/1/K system, etc.) will be explained. Finally, we summarize this lecture.
Requirements	The prerequisites for this class are Calculus and Linear Algebra. Familiarity with infinite series is desirable.
Grading Method	Students will be graded based on their report 20%, mini exam 20% and final exam 60% (or reports).
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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