M6444 Stochastic models II

Faculty of Science
Spring 2008 - for the purpose of the accreditation
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
RNDr. Marie Budíková, Dr. (lecturer)
Guaranteed by
prof. RNDr. Jana Jurečková, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: RNDr. Marie Budíková, Dr.
Prerequisites
M3121 Probability || M4122 Statistics
M5444
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 subject is about special case of stochastic processes - processes with continuos time, which has Markov property. Reflected are as finite, as countable Markov chains. Attention is paid also to queuing systems.
Syllabus
  • 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. Stochastic models in queuing theory: queuing systems and their classification, queuing systems with Poisson arrivals and exponential service times.
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
Assessment methods (in Czech)
Výuka se koná každý týden v rozsahu 2h přednáška, 1h cvičení. Zkouška je písemná.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.