Infopaket

Applications of Renewal Theory

Вибіркова дисципліна для ОП

First

2021/2022

7 Semester

3

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.

To successfully learn the discipline “Applications of Renewal Theory” 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 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.

The course “Applications of Renewal Theory” is aimed at applying results of Renewal Theory, learned by the student when attending the course “Advanced course of Analysis and Probability Theory. Block 1: Elements of Renewal Theory”, to renewal reward processes, renewal equations, regenerative processes, random walks with barrier, perturbed random walks and the Bernoulli sieve. The present course is a natural continuation of the disciplines “Calculus”, “Probability Theory” and “Advanced course of Analysis and Probability Theory. Block 1: Elements of Renewal Theory”.

1. Iksanov O.M. Elementy teoriyi vidnovlennya ta yiyi zastosuvannya: Elektronnyy navchalʹnyy posibnyk.-2022.-121 s. http://do.unicyb.kiev.ua/index.php/uk/2011-01-03-10-24-53/11-2011-01-03-10-44-09 2.Iksanov A. Renewal theory for perturbed random walks and similar processes. Cham: Birkhauser, 2016.-250 p. 3. Mitov K.V., Omey E. Renewal processes. Cham: Springer, 2014. -122 p. 4.Gut A. Stopped random walks: Limit theorems and applications. 2nd edition. New York: Springer-Verlag, 2009.—263 p.

Lectures, consultations, test works, independent work.

Intermediate assessment: 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