Completed course Analysis 1.
Probability 1
2025/2026
Programme:
Financial mathematics, First Cycle
Year:
2 year
Semester:
first
Kind:
mandatory
ECTS:
5
Language:
slovenian
Course director:
Lecturer (contact person):
Hours per week – 1. semester:
Lectures
2
Seminar
0
Tutorial
2
Lab
0
Content (Syllabus outline)
Basic combinatorics.
Outcome space, events, probability.
Conditional probability, formula for total probability.
Discrete random variables, distributions.
Joint discrete distributions.
Functions of discrete random variables.
Expectation and variance for discrete random variables.
Conditional distributions, conditional expectation.
Continuous random variables, densities, expectation.
Generating and moment generating functions.
Readings
- G. Grimmett, D. Stirzaker: Probability and random processes, 3rd ed., Oxford : Oxford University Press, 2001, 2009.
- D. Stirzaker: Probability and random variables : a beginner's guide, Cambridge : Cambridge University, cop. 1999.
Objectives and competences
Financial mathematics is based on probability theory. This course introduces basic concepts of probability needed for applications.
Intended learning outcomes
Understanding basic concepts of probability and the ability to do calculations with random variables and distributions effectively.
Learning and teaching methods
Lectures, problem sessions.
Assessment
2 midterms or written exam, oral exam
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)
Lecturer's references
Roman Drnovšek:
DRNOVŠEK, Roman. Spectral inequalities for compact integral operators on Banach function spaces. Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, 1992, let. 112, str. 589-598.
DRNOVŠEK, Roman. On invariant subspaces of Volterra-type operators. Integral equations and operator theory, ISSN 0378-620X, 1997, let. 27, št. 1, str. 1-9.
DRNOVŠEK, Roman. A generalization of Levinger's theorem to positive kernel operators. Glasgow mathematical journal, ISSN 0017-0895, 2003, vol. 45, part 3, str. 545-555.
Mihael Perman:
PERMAN, Mihael. An excursion approach to Ray-Knight theorems for perturbed Brownian motion. Stochastic Processes and their Applications, ISSN 0304-4149. [Print ed.], 1996, let. 63, str. 67-74. [COBISS-SI-ID 7621465]
PERMAN, Mihael, WELLNER, Jon A. On the distribution of Brownian areas. Annals of applied probability, ISSN 1050-5164, 1996, let. 6, št. 4, str. 1091-1111. [COBISS-SI-ID 7101017]
PERMAN, Mihael, WELLNER, Jon A. An excursion approach to maxima of the Brownian bridge. Stochastic Processes and their Applications, ISSN 0304-4149. [Print ed.], 2014, vol. 124, iss. 9, str. 3106-3120. [COBISS-SI-ID 17154393]
