Hiroshima University Syllabus

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Academic Year School/Graduate School Lecture Code 2021Year School of Integrated Arts and Sciences Department of Integrated Arts and Sciences ANM19001 Specialized Education 確率過程論 カクリツカテイロン Theory of Stochastic Processes KODAMA MEI コダマ　メイ Higashi-Hiroshima 3rd-Year,  First Semester,  2Term (2T) Thur5-8：IAS C808 Lecture My teaching style in this class is heavily depend on a blackboard. 2.0 J : Japanese 3 : Undergraduate High-Intermediate 25 : Science and Technology 01 : Mathematics/Statistics 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. "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. lesson 1: guidance, foundation of probability #1lesson 2:  foundation of probability #2lesson 3: probability space, random variablelesson 4: analytical theory of probabiity distributionlesson 5: independency and dependency of random variableslesson 6: foundation of the limit theorem lesson 7: random walklesson 8: Markov chain #1lesson 9: Markov chain #2lesson 10: counting processlesson 11: continuous-time Markov chains #1lesson 12: continuous-time Markov chains #2lesson 13: queuing sysem #1lesson 14: queuing sysem #2lesson 15: queuing sysem #3, conclusionreport, mini examination, final examination 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 Handouts, projector The 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, andthe basics of stochastic processes will be explained.No.4: one-dimensional distribution, discrete distribution, continuousdistribution, 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 largenumbers, 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 beexplained.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. The prerequisites for this class are Calculus and Linear Algebra.Familiarity with infinite series is desirable. Students will be graded based on their report 20%, mini exam 20% and final exam 60%. 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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