2021 Markov Analysis

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Academic unit or major
Undergraduate major in Mathematical and Computing Science
Nakano Yumiharu  Miyoshi Naoto 
Class Format
Media-enhanced courses
Day/Period(Room No.)
Tue7-8(W834)  Fri7-8(W834)  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
Language used
Access Index

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.


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 Poisson processes Understand the definition of Poisson processes and explain its basic properties.
Class 9 Compound Poisson processes Understand the definition of compound Poisson processes and explain its basic properties.
Class 10 Continuous time Markov chains Understand the definition of Markov chains in continuous time and explain its basic properties.
Class 11 Birth-death processes Explain the basic properties and applications of birth-death processes.
Class 12 Queueing systems Explain the basic properties and applications of queueing systems.
Class 13 Control of Markov chains Explain the basic approach to control problems of Markov chains and its applications.
Class 14 Brownian motion Introduction to Brownian motion

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.


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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