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MU:MU01120 Theory of Stochastic Processes - Course Information

## 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).
**Teacher(s)**- doc. RNDr. Michaela Mlíchová, Ph.D. (lecturer)
**Guaranteed by**- Mgr. Samuel Joshua Roth, Ph.D.

Mathematical Institute in Opava **Timetable**- Wed 8:05–8:50 R1
- Timetable of Seminar Groups:

*M. Mlíchová* **Prerequisites**(in Czech)- TYP_STUDIA ( B )
**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**- Mathematical Methods and Modelling (programme MU, Bc-M)
- Mathematical Methods in Economics (programme MU, Bc-M)
- Mathematical Methods in Risk Management (programme MU, Bc-M)
- General Mathematics (programme MU, Bc-M)

**Course objectives**- This course offers an in-depth treatment of the most common probability distributions and the theory of Markov chains.
**Syllabus**- - 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

- - probability, random variables, and cumulative distribution functions
**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

*required literature*- Š. Peško, J. Smieško.
*Stochastické modely operačnej analýzy*. Žilinská univerzita, Žilina, 1999. ISBN 80-7100-570-3. info

*recommended literature*- F. S. Hilier, G. J. Lieberman.
**Language of instruction**- Czech
**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.

- Enrolment Statistics (recent)

- Permalink: https://is.slu.cz/course/sumu/summer2021/MU01120