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Mathematical demography and modeling of random processes. Module 2. Modeling of random processes

Вибіркова дисципліна для ОП

First

2021/2022

6 Semester

2

Know and understand the basic methods of modeling random processes. Be able to calculate or evaluate basic numerical indicators for random processes. Demonstrate the ability to self-study and continue professional development. Be able to organize their own activities and get results within a limited time. Demonstrate skills of interaction with other people, ability to work in teams.

Full-time form

Know: basics of discrete mathematics, probability theory and mathematical statistics Be able to: formalize the conditions of problems and make a solution plan Have basic skills: solve typical problems in probability theory, mathematical statistics and discrete mathematics.

The discipline "Modeling of random processes" is an integral part of the cycle of professional training of specialists of educational and qualification level "bachelor"; it includes the study of basic random processes, namely, homogeneous and inhomogeneous Poisson processes, composite Poisson process, Gaussian processes, the study of different modeling methods for them. It is also mandatory to master the basic formulas and methods of their application. Particular attention is paid to the application of stochastic models of mathematics in the study of methods for generating random variables and processes. Students are introduced to the basic definitions, given the interpretation of formulas, and uses the software environment R to implement the above methods and build trajectories of random processes. Taught in the 6th semester, 75 hours. (2 ECTS credits), of which lectures - 34 hours, consultations - 1 hour, independent work - 40 hours. There are 2 content parts and an exam.

1. Kozachenko YV, Pashko AO, Rozora IV Modeling of random processes and fields: Monograph.- K .: VPC "Zadruga", 2007, 230p. 2. Mikhailov GA, Voytyshek AV Numerical statistical modeling. Methods of Monte Carlo.- M .: IC "Academy", 2006, 368p. 3. Ross, Sheldon M. Simulation.-2nd ed. Academic Press, 1997. 4. Buldygin VV, Kozachenko Yu.V. Metric characteristics of random variables and processes. - Kyiv.- TViMS, 1998. 5. Dovgai BV, Kozachenko YV, Slivka-Tilishchak GI Boundary value problems of mathematical physics with random factors: Monograph. - Kyiv: Kyiv University Publishing and Printing Center, 2008. - 173 p. 6. Gihman II, Skorokhod AV, Yadrenko M.Y. Probability theory and mathematical statistics.- K .: Higher School, 1979. 7. Yadrenko M.Y. Spectral theory of random fields.- K .: Higher School, 1980, 270p.

Lecture, individual work

Current assessment, control work, exams

Ukrainian