Infopaket

Modern problems of probability theory

ДВС.3.07

Вибіркова дисципліна для ОП

First

2023/2024

8 Semester

5

PLO21.3. Understand the fundamental areas of mathematics and computer science, to the extent necessary for learning mathematical disciplines, applied disciplines and using their methods in a chosen profession. PLO22.3. Understand the main areas of mathematical logic, theory of algorithms and computational theory, programming theory, probability theory and mathematical statistics. PLO23.3. Be able to use professional knowledge, skills and abilities in the field of fundamental sections of mathematics and computer science for research of real processes of different nature. PLO24.3. Be able to independently analyze the relevant subject area, be able to develop mathematical and structural algorithmic models.

Full-time form

To successfully learn the discipline “Stochastic models of applied mathematics. M.1. Statistical modelling. M.2. Optimal stopping of Markov chains” the student should satisfy the following requirements. They know (a) fundamentals of mathematical methods for construction, verification and investigation of qualitative characteristics of deterministic and stochastic mathematical models; (b) classical methods of Calculus, Algebra and Probability Theory. They can (a) investigate qualitative characteristics of available mathematical models; (b) apply classical methods for solving applied problems in deterministic and stochastic models. They should be able to (a) apply classical methods of Calculus and Probability Theory; (b) seek information in open sources and properly analyze it.

Monte Carlo method. Pseudorandom numbers. Role of mathematical statistics. Modelling of discrete random variables. Effectiveness of standard method. Modelling of continuous random variables. Modelling of random vectors. Modelling of random processes and queueing systems. Solution of the problems of mathematical physics by means of statistical modeling. Secretary problem. Optimal stopping of Markov chain. Payoff function. Optimal strategy. Game value. Excessive functions. Support set.

1. R.L. Graham, D.E. Knuth, O. Patashnik, Concrete Mathematics - a Foundation for Computer Science, 2nd ed., Addison-Wesley, 1994. – 670 p. 2. Luc Devroye. Non-uniform random variate generation. 1986. – 857 p. 3. Averill M. Law, W. David Kelton. Simulation modeling & analysis. 1991. – 155 p. 4. V.V. Nekrutkin. Modelirovaniye raspredeleniy. Materialy spetsial'nogo kursa i spetsial'nogo seminara. 2013. – 90 s. 5. Carl Graham, Denis Talay. Stochastic Simulation and Monte Carlo Methods. 2013. – 260 p. 6. Soren Asmussen Peter W. Glynn.Stochastic Simulation: Algorithms and Analysis 2007 Springer. – 476 p. 7. Christian Walck . Hand-book on statistical distributions for experimentalists. 2007. – 202 p. 8. Ye. B. Dynkin, A. A. Yushkevich. Teoremy m zadachi o protsessakh Markova. 1967. – 231 c. 9. M. Babaioff, N. Immorlica, D. Kempe, R. Kleinberg. Matroid secretary problems, J. ACM 65 (6) (2018) 35 p.. 10. Berezovskiy B.A., Gnedin A.V. Zadacha nailuchshego vybora. 1984. – 202 c.

Lectures, seminars, consultations, test works, independent work.

Intermediate assesement: The maximal number of available points is 60. Test work no. 1: 30/18 points. Test work no. 2: 30/18 points. Final assessment (in the form of exam): The maximal number of available points is 40. The form of exam: writing. The types of assignments are 4 writing assignments (2 theoretical and 2 practical).

Ukrainian