2022 | Markov Analysis - TOKYO TECH OCW

2022　Markov Analysis

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Academic unit or major: Undergraduate major in Mathematical and Computing Science

Instructor(s): Nakano Yumiharu Miyoshi Naoto

Class Format: Lecture (On-demand)

Media-enhanced courses

Day/Period(Room No.): On-demand()

Group: -

Course number: MCS.T312

Credits: 2

Academic year: 2022

Offered quarter: 2Q

Syllabus updated: 2022/4/4

Lecture notes updated: -

Language used: Japanese

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Syllabus

Course description and aims

This course facilitates students in understanding of the fundamentals of Markov processes, one of most basic stochastic processes, through analyses of stochastic models.

Student learning outcomes

At the end of this course, students will be able to:
1) Have understandings of the concept of Markov property in discrete and continuous time, and the basic facts that hold in Markov processes.
2) Apply the theory of Markov processes to analyze various stochastic models.

Keywords

Markov processes, stochastic models, Markov chains, Poisson processes

Competencies that will be developed

✔ Specialist skills

Intercultural skills

Communication skills

Critical thinking skills

✔ Practical and/or problem-solving skills

Class flow

The class will be conducted on demand using video. The first 30 minutes of each class will be spent on Zoom, explaining the contents of the class to be delivered on the day, reviewing the previous class, explaining the previous assignment, and answering questions. Use T2SCHOLA as a place to ask questions and exchange opinions.

Course schedule/Required learning

	Course schedule	Required learning
Class 1	Markov property and discrete time Markov chains	Explain the concept of Markov properties.
Class 2	Transition diagram and probability distributions of the state	Explain the transition diagram and probability distribution of the state.
Class 3	Classification of the state: connectivity	Classificate the state of Markov chains.
Class 4	Periodicity	Explain the concept and basic facts of the periodicity.
Class 5	Reccurence	Explain the concept and basic facts of the recurrence.
Class 6	Stationary distributions	Explain the concept of the stationary distributions and its derivation.
Class 7	Limit theorems	Explain the limit theorems.
Class 8	Markov chain Monte Carlo methods	Introduce Markov chain Monte Carlo methods.
Class 9	Poisson processes	Understand the definition of Poisson processes and explain its basic properties.
Class 10	Compound Poisson processes	Understand the definition of compound Poisson processes and explain its basic properties.
Class 11	Continuous time Markov chains	Understand the definition of Markov chains in continuous time and explain its basic properties.
Class 12	Birth-death processes	Explain the basic properties and applications of birth-death processes.
Class 13	Queueing systems	Explain the basic properties and applications of queueing systems.
Class 14	Brownian motion	Introduction to Brownian motion

Textbook(s)

Lecture notes.

Reference books, course materials, etc.

P. Brémaud, Markov Chains: Gibbs Fields, Monte Carlo Simulation, and Queues, Springer

Assessment criteria and methods

Students will be assessed on the understanding of Markov processes and its application. Grades are based on exercises and a final exam.

Related courses

MCS.T212 ： Fundamentals of Probability

Prerequisites (i.e., required knowledge, skills, courses, etc.)

It is preferable that students have completed MCS.T212:Fundamentals of Probability.

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