M5444 Stochastic models I

Faculty of Science
Autumn 2011 - acreditation

The information about the term Autumn 2011 - acreditation is not made public

Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
Teacher(s)
RNDr. Marie Budíková, Dr. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M3121 Probability and Statistics I || M4122 Probability and Statistics II
M3121 and M4122
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
This course deals with a special case of stochastic processes - processes with Markov property which time parameter has only values from the set of natural numbers. Attention is paid to both theoretical basics and practical applications. Upon completing this course, students will be able to simulate simple real-world situations using homogeneous Markov’s chains with discrete or continuous time. They also will be able to use MATLAB system.
Syllabus
  • Introduction to study of stochastic processes, functional characteristics of stochastic process.
  • Markov chains with discrete time: the transition probabilities, classification of states, irreducible and reducible chains, stationary distribution, transient states, estimates of the probability of transition, Markov chains with estimation of transitions, Markov chains with disconted estimation of transitions
  • Finite Markov chains with continuos time: basic references, Chapman-Kolmogorov's equality, Kolmogorov's differential equations and their solving, limited division of states.
  • Countable Markov chains with continuos time: solution of Kolmogorov's equations for countable chains, limited division of states for countable chains, Poisson's process, Yule's process, general process of birth, linear process of birth and death, general process of birth and death.
Literature
  • KOŘENÁŘ, Václav. Stochastické procesy. Vyd. 1. Praha: Vysoká škola ekonomická v Praze, 2002, 227 s. ISBN 8024503115. info
  • PRÁŠKOVÁ, Zuzana and Petr LACHOUT. Základy náhodných procesů. 1. vyd. Praha: Karolinum, 1998, 146 s. ISBN 8071846880. info
  • MANDL, Petr. Pravděpodobnostní dynamické modely. 1. vyd. Praha: Academia, 1985, 181 s. info
Teaching methods
The weekly class schedule consists of 2 hour lecture and 1 hour of class exercises with MATLAB system.
Assessment methods
The examination is written.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.