MU01120 Theory of Stochastic Processes

Mathematical Institute in Opava
Winter 2018
Extent and Intensity
1/1/0. 3 credit(s). Type of Completion: z (credit).
Teacher(s)
Mgr. Samuel Joshua Roth, Ph.D. (lecturer)
Mgr. Samuel Joshua Roth, Ph.D. (seminar tutor)
Guaranteed by
Mgr. Samuel Joshua Roth, Ph.D.
Mathematical Institute in Opava
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
In view of the fact that this elective subject can be inscribed already in the first year, the teaching style is simple and understandable. After the basic informations about probability theory it follows practical stochastic dynamics.
Syllabus
  • - the probability notion, random variable and its cumulative distribution function
    - 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
Literature
    recommended literature
  • Š. Peško, J. Smieško. Stochastické modely operačnej analýzy. Žilinská univerzita, Žilina, 1999. ISBN 80-7100-570-3. info
  • 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
Language of instruction
English
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
Teacher's information
The pre-exam credit will be obtained after a writing test.
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 2019, Winter 2020, Summer 2021, Summer 2022, Summer 2023, Summer 2024.
  • Enrolment Statistics (Winter 2018, recent)
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