Course: Markov Processes

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Course title Markov Processes
Course code KMA/MP
Organizational form of instruction Lecture + Exercise
Level of course Master
Year of study not specified
Semester Summer
Number of ECTS credits 3
Language of instruction Czech
Status of course Compulsory-optional, Optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Müller Ivo, RNDr. PhDr. Ph.D.
Course content
1 Generating function of a random variable. 2 Recurring events, time to return. 3 Limiting behavior of a recurring event, delayed recurring events. 4 Probabilities of transition, homogenous chains. 5 Classification of states, theorems on different types of states. 6 Stationary distribution, probabilities of absorption. 7 Markov chains with continuous time. 8 Finite chains: stationary distribution, intensities of transition. 9 Kolmogorov differential equations. 10 Examples of finite chains. 11 Countable chains: stationary distribution. 12 Poissson process, Yule process.

Learning activities and teaching methods
Lecture
  • Attendace - 39 hours per semester
  • Preparation for the Course Credit - 20 hours per semester
  • Preparation for the Exam - 30 hours per semester
Learning outcomes
Modeling of dependant events through transitional probabilities.
Comprehension Modeling of dependant events through transitional probabilities.
Prerequisites
Motivation to learn

Assessment methods and criteria
Oral exam, Written exam

Credit: active participation in seminars, written test. Exam: oral.
Recommended literature
  • W. Feller. (1966). An Introduction to Probability Theory and its Applications. Wiley.
  • V. Dupač, J. Dupačová. (1980). Markovovy procesy I, II. skripta MFF UK.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester