2025/2026
Дополнительные главы теории вероятностей
Статус:
Маго-лего
Где читается:
Факультет компьютерных наук
Когда читается:
1 модуль
Охват аудитории:
для своего кампуса
Язык:
английский
Контактные часы:
28
Course Syllabus
Abstract
This course establishes the rigorous measure-theoretic foundations of modern probability. Key concepts include the construction of probability measures, advanced integration for expectation, and the classification of stochastic convergence. The course concludes with fundamental theorems that are critical for understanding and advancing statistical and stochastic analysis.
Learning Objectives
- This course aims to understand probability theory through the lens of measure and integration, analyzing sequence convergence modes, and comprehending the definition of conditional expectation.
Expected Learning Outcomes
- The ability to rigorously define expectation and work with its properties via Lebesgue integration.
- Proficiency in manipulating conditional expectation and identifying density functions via the Radon-Nikodym theorem.
- The ability to justify the construction of stochastic processes using Kolmogorov's theorem.
- Understanding the mathematical foundations of measurable functions and sets.
- Understanding the mathematical foundations of expectation, different types of convergence, and conditional expectation.
Course Contents
- Measure extension
- Expectation
- Types of Convergence
- Conditional Expectation
- Kolmogorov's Extension Theorem
Bibliography
Recommended Core Bibliography
- Damien Lamberton, & Bernard Lapeyre. (2011). Introduction to Stochastic Calculus Applied to Finance: Vol. 2nd ed. Chapman and Hall/CRC.
- Foundations of modern probability, Kallenberg, O., 2002
Recommended Additional Bibliography
- Chaumont, L., & Yor, M. (2012). Exercises in Probability : A Guided Tour From Measure Theory to Random Processes, Via Conditioning (Vol. 2nd ed). Cambridge: Cambridge University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=466664
- Measure theory and filtering : introduction and applications, Aggoun, L., 2012