Oct 18, 2019   11:57 a.m. Lukáš
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Course syllabus D1-SPM - Stochastic processes and models (FCE - 2019/2020 - post-graduate studies)


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University: Slovak University of Technology in Bratislava
Faculty: Faculty of Civil Engineering
Course unit code: D1-SPM
Course unit title: Stochastic processes and models
Mode of delivery, planned learning activities and teaching methods:
workshop2 hours weekly / 26 hours per semester of study (on-site method)

 
Credits allocated: 5
 
Recommended semester/trimester: Applied Mathematics - doctoral (semi-compulsory), 1. year
Applied Mathematics (in english language) - doctoral (semi-compulsory), 1. year
Level of study: 3.
Prerequisites for registration: none
 
Assesment methods:
seminar project, exam
 
Learning outcomes of the course unit:
Students will get information about the major parts of classical probability theory and probabilities on fuzzy systems, including MV-algebras, as well as on basic types of random processes and time series. Several applications in stochastic systems will be shown, such as the mass theory. Finally, the basics of linear stochastic differential equations will be taught.
 
Course contents:
- Probability theory, limit theorems, conditional distributions.
- Random vectors, multidimensional normal distribution, characteristic functions, several kinds of convergences, probability theory on fuzzy sets.
- Markov chains, Kolmogorov equations, classification of states and chains, applications.
- Continuous Markov chains, exponential distribution, Poisson process, convolution of exponetial distributions, first models in mass theory.
- Basic classification of random processes, stationarity, Wiener process.
- Basics of stochastic analysis, Gaussian processes, ergodicity, Itô formula.
 
Recommended or required reading:
Basic:
KALINA, M. -- BACIGÁL, T. -- SCHIESSLOVÁ, A. Základy pravdepodobnosti a matematickej štatistiky. Bratislava : STU v Bratislave, 2010. 216 p. ISBN 978-80-227-3273-4.
ANDĚL, J. Matematika náhody. Praha : Matfyzpress, 2003. 273 p. ISBN 80-86732-07-X.
ROSS, S M. Introduction to probability models. San Diego : Academic Press, 1997. 669 p. ISBN 0-12-598470-7.
GRIMMETT, G. -- STIRZAKER, D. Probability and Random Processes. USA: Oxford University Press, 2001. 608 p.

 
Language of instruction: slovak and english or english
 
Notes:
 
Courses evaluation:
Assessed students in total: 2

PN
100,0 %0 %
Name of lecturer(s): prof. RNDr. Martin Kalina, PhD. (examiner, instructor, lecturer, tutor) - slovak, english
prof. RNDr. Radko Mesiar, DrSc. (person responsible for course)
 
Last modification: 31. 10. 2017
Supervisor: prof. RNDr. Radko Mesiar, DrSc. and programme supervisor


Last modification made by Ing. Peter Korčák on 10/31/2017.

Type of output: