Course detail

Stochastic Processes

FEKT-FNPRAcad. year: 2010/2011

The course provides the introduction to the theory of stochastic processes. The following topics are dealt with: types and basic characteristics, discrete-time and continuous-time Markov chains including their analysis.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

doc. RNDr. Zdeněk Šmarda, CSc.

Department

Department of Mathematics (UMAT)

Learning outcomes of the course unit

The ability of orientation in the basic problems of the theory of stochastic processes and the ability to apply the basic methods and algorithms. Solving problems in the areas cited in the annotation above by using contemporary mathematical software.

Prerequisites

The subject knowledge on the Bachelor's degree level is requested.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

Assesment methods and criteria linked to learning outcomes

Requirements for completion of a course are specified by a rgulation issued by the lecturer responsible for the course and updated for every year.

Course curriculum

Stochastic processes. Characteristics of stochastic processes. Discrete-time Markov chains. Homogeneous and regular Markov chains.
Chapman-Kolmogorov equations. Analysis of Markov chains by using Z-transformation. Continuous-time Markov chains. Chapman-Kolmogorov differential equations. Poisson process.

Work placements

Not applicable.

Aims

The aim of the course is to present survey of basic notions and results in the field of the theory of stachastic processes and to apply theoretical procedures on simulated or real data by using mathematical software.

Specification of controlled education, way of implementation and compensation for absences

Limitations of controlled teaching and its procedures are specified by a regulation issued by the lecturer responsible for the course and updated for every year.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Not applicable.

Recommended reading

Ito, K., Stochastic Processes, Springer, 2004, ISBN 3-540-20482-2
Kropáč, J., Vybrané partie z náhodných procesů a matematické statistiky, Vojenská akademie v Brně, 2002, S-1971.
Prášková, Z., Lachout, P., Základy náhodných procesů, Univerzita Karlova, Praha, 1998, ISBN 80-7184-588-0

Classification of course in study plans

  • Programme BTBIO-F Master's

    branch F-BTB , 1 year of study, winter semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

doc. RNDr. Jaromír Baštinec, CSc.

Syllabus

1. Random variables, basic notions.
2. Stochastic processes, characteristics of stochastic processes.
3. Discrete-time Markov chains, Chapman-Kolmogorov equations.
4. Homogeneous Markov chains.
5. Regular Markov chains.
6. Absorption chains.
7. Z-transformation, analysis of Markov chains.
8. Continuous-time Markov chains.
9. Poisson process.
10. Chapman-Kolmogorov differential equations.
11. Markov decision processes.
12. Asymptotical properties of Markov chains.
13. Decision process with alternatives.

Exercise in computer lab

26 hod., compulsory

Teacher / Lecturer

doc. RNDr. Jaromír Baštinec, CSc.

Syllabus

1. Introduction to statistic software.
2. Analysis of random variables.
3. Calculation of characteristics of random variables.
4. Discrete-time Markov chains-applications.
5. Applications and solving of Chapman-Kolmogorov equations.
6. Homogeneous and regular Markov chains-applications.
7. Applications of absorption chains.
8. Analysis of Markov chains by using Z-transformation.
9. Characteristics of continuous-time Markov chains.
10. Applications of the Poisson process.
11. Applications and solving of Chapman-Kolmogorov differential equations.
12. Analysis of Markov decision processes.
13. Asymptotic analysis of Markov chains.