Hiroshima University Syllabus |

Japanese

Academic Year 2021Year 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

EnglishTheory 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. Credits 2.0 Class Hours/Week Language on Instruction J : Japanese Course Level 3 : Undergraduate High-Intermediate Course Area（Area） 25 : Science and Technology Course Area（Discipline） 01 : Mathematics/Statistics Eligible Students Keywords Special Subject for Teacher Education Special Subject Class Status

within Educational

ProgramCriterion referenced

EvaluationIntegrated 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 examinationText/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

Learning techniques to be incorporated Suggestions on

Preparation and

ReviewThe materials will be used in Bb9 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, queing 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%. 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.