Hiroshima University Syllabus

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Academic Year School/Graduate School Lecture Code 2022Year School of Informatics and Data Science KA224001 Specialized Education 確率過程論 カクリツカテイロン Stochastic Processes SHIMA TADASHI シマ　タダシ Higashi-Hiroshima 3rd-Year,  Second Semester,  4Term (4T) Tues5-6,Thur5-6：IAS K209 Lecture My teaching style in this class is heavily depend on a blackboard. 2.0 B : Japanese／English 3 : Undergraduate High-Intermediate 25 : Science and Technology 01 : Mathematics/Statistics measure theory, probability, stochastic processes, Brownian motion 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. "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 probabilityand basic concepts of the theory of stochastic processesand to develop their problem-solving skills. 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 tothe 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, 培風館確率論，舟木直久，朝倉書店 the textbook will be indicated in the class. In each class, I submit some problems as exercises.So, review and try to solve them. The prerequisites for this course are Calculus and introductory probability theory. Students will be graded based on their report. 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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