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master's thesis
Regularno varirajuće funkcije i primjene u vjerojatnosti
2021. urn:nbn:hr:126:982127
Bastijan, Tea
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics and Mathematics Teaching
Probability, Mathematical Statistics and Data Science Research Group

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Bastijan, T. (2021). Regularno varirajuće funkcije i primjene u vjerojatnosti (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:982127

Bastijan, Tea. "Regularno varirajuće funkcije i primjene u vjerojatnosti." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2021. https://urn.nsk.hr/urn:nbn:hr:126:982127

Bastijan, Tea. "Regularno varirajuće funkcije i primjene u vjerojatnosti." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2021. https://urn.nsk.hr/urn:nbn:hr:126:982127

Bastijan, T. (2021). 'Regularno varirajuće funkcije i primjene u vjerojatnosti', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 06 April 2025, https://urn.nsk.hr/urn:nbn:hr:126:982127

Bastijan T. Regularno varirajuće funkcije i primjene u vjerojatnosti [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2021 [cited 2025 April 06] Available at: https://urn.nsk.hr/urn:nbn:hr:126:982127

T. Bastijan, "Regularno varirajuće funkcije i primjene u vjerojatnosti", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2021. Available at: https://urn.nsk.hr/urn:nbn:hr:126:982127

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Metadata
TitleRegularno varirajuće funkcije i primjene u vjerojatnosti
Title (english)Regulary Variating Functions and Applications to Probability
AuthorTea Bastijan
MentorDanijel Grahovac (mentor)
Committee memberMirta Benšić (predsjednik povjerenstva)
Committee memberDanijel Grahovac (član povjerenstva)
Committee memberNenad Šuvak (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Pure Mathematics and Mathematics Teaching)
(Probability, Mathematical Statistics and Data Science Research Group)
Osijek
Defense date and country2021-05-31, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Probability Theory and Statistics
Abstract
U ovome radu definirali smo sporo, odnosno regularno varirajuće funkcije i naveli nekoliko primjera. Iskazali smo i dokazali njihova osnovna svojstva medu kojima su najvažniji Karamatin teorem i Karamatin Tauberovski teorem. Drugi dio rada bavi se primjenama u vjerojatnosti. Vidjeli smo nekoliko svojstava transfomacija funkcija distribucija koja dobivamo primjenom Karamatinog Tauberovskog teorema. Proučavali smo slabu konvergenciju normalizirane sume, odnosno maksimuma nezavisnih i jednako distribuiranih slučajnih varijabli.
Abstract (english)
In this paper we defined slowly and regularly varying functions and gave a few examples. We stated and proved their basic properties, among which the most important are Karamata's theorem and Karamata's Tauberian theorem. The second part of the paper deals with application in probability. We saw several properties of the transformed distribution function which we obtain by applying the Karamata's Tauberian theorem. We studied weak convergence of the normalized sum, i.e., the maximum of independent and equally distributed random variables.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:982127
Study programmeTitle: Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Course: Financial and Statistical Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2021-06-01 11:20:29