Infopaket

Advanced course of Analysis and Probability Theory

ВК.3.02

Вибіркова дисципліна для ОП

First

2024/2025

6 Semester

4

LO18. To communicate effectively regarding information, ideas, problems and solutions with specialists and society, in general. 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 Advanced course of Analysis and Probability 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; (c) analуze the nature and goals of construction of mathematical structures and 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 discipline is aimed at learning basic results of Renewal Theory for random walks with nonnegative steps and mastering technical tools which are intrinsic to this subject area. The subject matter includes classical theorems of Renewal Theorem like the elementary renewal theorem, Blackwell’s theorem, the key renewal theorem, the strong law of large numbers for the number of renewals. The present course is a natural continuation of the disciplines “Calculus” and “Probability Theory”.

1. Iksanov O.M. Elements of renewal theory, with applications: Electronic lecture notes. -2024. -121 p. https://do.csc.knu.ua/wp-content/uploads/2023/01/LN_renewal.pdf 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. 5. Asmussen S. Applied probability and queues. New York: Springer, 2003. – 438 p. 6. Resnick S. Adventures in stochastic processes. Boston: Birkhauser, 1992.—626 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