Hiroshima University Syllabus

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Academic Year School/Graduate School Lecture Code 2024Year 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：IAS K204, (4T) Thur5-6：IAS K208 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 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. "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 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，朝倉書店確率論,  岩田耕一郎, 森北出版 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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