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DS2STM - Stohasticki modeli

Course specification
Course title
Acronym DS2STM
Study programme Electrical Engineering and Computing
Module
Type of study doctoral studies
Lecturer (for classes)
Lecturer/Associate (for practice)
    Lecturer/Associate (for OTC)
      ESPB 9.0 Status elective
      Condition Mathematics on the level of compulsory courses at ETF. Probability and Statistics on the level of one semester course (with possibility of taking a prerequisite test if does not have formal conditions fulfilled). Familiarity with Lebesgue integration and corresponding theory is desirable, but not obligatory.
      The goal Stochastic modelling is a wide area, not only by various applications in different fields, but also by richness of mathematics that it uses. The goal of this course is to enable a student for researsh in the topic of his/her dissertation.Hence,the ultimate purpose of this course is to make a student familiar with some of numerous models and to learn to use the tools of stochastic modelling.
      The outcome The student will be able to to read and understand scientific literature related to the relevant stochastic models, as well as to apply the acquired knowledge for model making and testing based on data.
      Contents
      Contents of lectures Conditional distributions, prediction. Linear regression.Monte Carlo methods. Stochastic processes.Poisson process.Brownian motion. Martingales in discrete and continuous time.Markov processes. Ito formula and stochastic calculus.Continuation (A or B) A: Girsanov's theory, change of measure and applications; B: Markov processes and some applications, MCMC (Markov Chain Monte Carlo) methods.
      Contents of exercises
      Literature
      1. Milan Merkle, Verovatnoća i statistika za inženjere i studente elektrotehnike, Akademska misao, Beograd 2010.
      2. J. Michael Steele, Stochastic Calculus and Financial Applications, Springer 2001.
      3. Oliver Ibe, Markov Processes for Stochastic Modeling, Elsevier/Academic Press 2009.
      4. Peter Guttorp, Stochastic Modelling of Scientific Data, Chapman&Hall, 1995.
      5. B. Oksendal, Stochastic differential equations. An introduction with applications. Fiftth corrected printing of the sixth edition, Springer, 2010.
      Number of hours per week during the semester/trimester/year
      Lectures Exercises OTC Study and Research Other classes
      6
      Methods of teaching Lectures and consultations.
      Knowledge score (maximum points 100)
      Pre obligations Points Final exam Points
      Activites during lectures Test paper 30
      Practical lessons Oral examination
      Projects
      Colloquia
      Seminars 70