1. komponenta

Lecture type	Total
Lectures	45

COURSE AIMS AND OBJECTIVES: To acquaint students with the fundamental results and ideas of probability theory. To train students to be able to understand and follow contemporary literature in statistics and data science

COURSE DESCRIPTION AND SYLLABUS:
1. Introduction: Sigma algebras and rings. Measure and probability.
2. Random variables and their distributions: Distributions of random variables and vectors. Integrals and expectations of random variables. Independence. Borel-Cantelli lemmas and Kolmogorov's law 0-1.
3. Moment and laws of large numbers: Moments, moment inequalities and convergence of random variables. The weak law of large numbers. The strong law of large numbers.
4. Convergence in distribution and coupling: The concept of coupling. Convergence in distribution and in total variation. Chen-Stein method. Convergence towards the Poisson distribution. Convergence towards the Normal distribution. Extensions and applications of central limit theorems. Cramer-Wold device.
5. Additional topics: Applications of probability models. Introduction to the theory of large deviations.

1. Probability and measure, Billingsley, Patrick, John Wiley & Sons, 2008.
2. Teorija vjerojatnosti, Sarapa, Nikola, Školska knjiga, 2002.
3. Probability: an introduction, Grimmett, Geoffrey, and Dominic Welsh, Oxford University Press, 2014.
4. Probability: theory and examples. Vol. 49, Durrett, Rick, Cambridge university press, 2019.

Mandatory course - Regular study - Financial and Business Mathematics