Probability

Completed courses Analysis 1 and Analysis 2.

definition of probability
conditional probability
random variables and vectors
discrete and continuous distributions
expectation
variance, covariance and correlation coefficient
higher moments and order statistics
conditional distribution and conditional expectation
generating functions
laws of large numbers

1. M. Hladnik: Verjetnost in statistika , založba FE in FRI, Ljubljana, 2002, , ISBN: 961-6209-34-5, 140 str.
2. R. Jamnik: Matematična statistika, DZS, Ljubljana, 1980, 408 str.
3. R. Jamnik: Verjetnostni račun in statistika, DMFA Slovenije, Ljubljana, 1986, 1995, 156 str.
4. G. Grimmett, D. Stirzaker: Probability and random processes, 3rd ed., Oxford University Press, Oxford, 2001, 2009, 541 str.

Introduction to probability theory.

Understanding of theoretical concepts in various applications. The ability to recognize probabilistic concepts in other sciences (physics, economics, finance, actuarial science, medicine, biology, industrial statistics).

Lectures, exercises, homeworks.

written examination
theoretical test or oral exam
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Roman Drnovšek:
– DRNOVŠEK, Roman. Triangularizing semigroups of positive operators on an atomic normed Riesz space. Proceedings of the Edinburgh Mathematical Society, ISSN 0013-0915, 2000, let. 43, št. 1, str. 43-55 [COBISS-SI-ID 9480281]
– DRNOVŠEK, Roman. Common invariant subspaces for collections of operators. Integral equations and operator theory, ISSN 0378-620X, 2001, vol. 39, no. 3, str. 253-266 [COBISS-SI-ID 10597721]
– DRNOVŠEK, Roman. An infinite-dimensional generalization of Zenger's lemma. Journal of mathematical analysis and applications, ISSN 0022-247X. [Print ed.], 2012, vol. 388, iss. 2, str. 1233-1238 [COBISS-SI-ID 16214617]
Mihael Perman:
– PERMAN, Mihael, SENEGAČNIK, Andrej, TUMA, Matija. Semi-Markov models with an application to power-plant reliability analysis. IEEE transactions on reliability, ISSN 0018-9529, 1997, vol. 46, no. 4, str. 526-532 [COBISS-SI-ID 2567707]
– 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, PITMAN, Jim, YOR, Marc. Size-biased sampling of Poisson processes and excursions. Probability theory and related fields, ISSN 0178-8051, 1992, 92, no. 1, str. 21-39 [COBISS-SI-ID 12236377]
Matija Vidmar:
– VIDMAR, Matija, WARREN, Jon. Stationary local random countable sets over the Wiener noise. Probability theory and related fields. Apr. 2024, vol. 188, iss. 3/4, str. 1063-1129. ISSN 0178-8051. https://link.springer.com/article/10.1007/s00440-023-01227-3, Repozitorij Univerze v Ljubljani – RUL, DOI: 10.1007/s00440-023-01227-3. [COBISS-SI-ID 166137603], [Odprti dostop]
projekt: P1-0402-2019 Matematična fizika; financer: Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije
– FOUCART, Clément, VIDMAR, Matija. Continuous-state branching processes with collisions: first passage times and duality. Stochastic Processes and their Applications. [Print ed.]. Jan. 2024, vol. 167, [article no.] 104230, 35 str. ISSN 0304-4149. https://www.sciencedirect.com/science/article/pii/S0304414923002028, Repozitorij Univerze v Ljubljani – RUL, DOI: 10.1016/j.spa.2023.104230. [COBISS-SI-ID 170650115], [Odprti dostop]
projekt: N1-0174-2021 Časi prvih prehodov eno-stranskih procesov Markova; financer: Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije
projekt: P1-0402-2019 Matematična fizika; financer: Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije
– VIDMAR, Matija. Complete monotonicity of time-changed Lévy processes at first passage. Statistics & probability letters. Feb. 2023, vol. 193, art. 109710 (9 str.). ISSN 0167-7152. https://www.sciencedirect.com/science/article/pii/S0167715222002231, Repozitorij Univerze v Ljubljani – RUL, DOI: 10.1016/j.spl.2022.109710. [COBISS-SI-ID 127643395]