MU01120 Theory of Stochastic Processes

Mathematical Institute in Opava
Summer 2021
Extent and Intensity
1/1/0. 3 credit(s). Type of Completion: z (credit).
doc. RNDr. Michaela Mlíchová, Ph.D. (lecturer)
Guaranteed by
Mgr. Samuel Joshua Roth, Ph.D.
Mathematical Institute in Opava
Wed 8:05–8:50 R1
  • Timetable of Seminar Groups:
MU01120/01: Wed 8:55–9:40 R1, M. Mlíchová
Prerequisites (in Czech)
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 offers an in-depth treatment of the most common probability distributions and the theory of Markov chains.
  • - probability, random variables, and cumulative distribution functions
    - discrete and continuous random variables
    - expectation and variance
    - binomial, Poisson, exponential, and normal probability distributions
    - stochastic process, an example of inventory policy
    - discrete Markov chain with finite state space
    - Chapman-Kolmogorov equations
    - classification of states of a Markov chain
    - first passage time
    - steady-state probabilities of Markov chain
    - continuous Markov chains
    - basic queueing models
    required literature
  • F. S. Hilier, G. J. Lieberman. Introduction to stochastic models in operations reseach. McGraw Hill, 1990. info
  • Z. Riečanová a kol. Numerické metody a matematická štatistika. Alfa, Bratislava, 1987. ISBN 063-559-87. info
    recommended literature
  • Š. Peško, J. Smieško. Stochastické modely operačnej analýzy. Žilinská univerzita, Žilina, 1999. ISBN 80-7100-570-3. info
Language of instruction
Further comments (probably available only in Czech)
Study Materials
The course can also be completed outside the examination period.
Teacher's information
Conditions for successful course completion:
1. Satisfactory oral presentation of at least 15 solved homework problems during tutorials.
2. Satisfactory completion of the semester project, which will be assigned during the first tutorial.
The course is also listed under the following terms Winter 1999, Winter 2000, Winter 2001, Winter 2002, Winter 2003, Winter 2004, Winter 2005, Winter 2006, Winter 2007, Winter 2008, Winter 2009, Winter 2010, Winter 2011, Winter 2012, Winter 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018, Winter 2019, Winter 2020.
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