Information sheet ECTS Syllabus
Course syllabus D1-SPM - Stochastic processes and models (FCE - 2018/2019 - post-graduate studies)
|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:|
|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|
|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.|
|- 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:|
|Language of instruction:||slovak and english or english|
|Assessed students in total: 2|
|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. 8. 2015|
|Supervisor:||prof. RNDr. Radko Mesiar, DrSc. and programme supervisor|
Last modification made by Ing. Peter Korčák on 08/31/2015.