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master's thesis
Zakon ponovljenog logaritma
2024. urn:nbn:hr:126:191950
Brlek, Dora
Josip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics

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Brlek, D. (2024). Zakon ponovljenog logaritma (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:191950

Brlek, Dora. "Zakon ponovljenog logaritma." Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. https://urn.nsk.hr/urn:nbn:hr:126:191950

Brlek, Dora. "Zakon ponovljenog logaritma." Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. https://urn.nsk.hr/urn:nbn:hr:126:191950

Brlek, D. (2024). 'Zakon ponovljenog logaritma', Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, accessed 26 December 2024, https://urn.nsk.hr/urn:nbn:hr:126:191950

Brlek D. Zakon ponovljenog logaritma [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics; 2024 [cited 2024 December 26] Available at: https://urn.nsk.hr/urn:nbn:hr:126:191950

D. Brlek, "Zakon ponovljenog logaritma", Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, Osijek, 2024. Available at: https://urn.nsk.hr/urn:nbn:hr:126:191950

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Metadata
TitleZakon ponovljenog logaritma
Title (english)The Law Of The Iterated Logarithm
AuthorDora Brlek
MentorDanijel Grahovac (mentor)
Committee memberMirta Benšić (predsjednik povjerenstva)
Committee memberDanijel Grahovac (član povjerenstva)
Committee memberNenad Šuvak (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics
Osijek
Defense date and country2024-10-28, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Probability Theory and Statistics
Abstract
Na početku diplomskog rada definiraju se pojmovi iz teorije vjerojatnosti koji se spominju tijekom čitavog rada i potrebni su za dokaz zakona ponovljenog logaritma. Uz to, navode se zakoni nula-jedan, zakoni velikih brojeva te centralni granični teorem. Nakon toga slijedi dokaz gornje eksponencijalne granice te iskaz Borel-Cantellijeve leme koji su potrebni za dokaz zakona ponovljenog logaritma. Zatim, uz neke dodatne pomoćne tvrdnje, se dokazuje zakon ponovljenog logaritma. Na samom kraju rada, navodimo nekoliko proširenja zakona ponovljenog logaritma te na koji način vrijedi na različitim vrstama podnizova.
Abstract (english)
The thesis starts with the definition of basic terms from probability theory that are used through the thesis and are necessary for the proof of the law of iterated logarithm. In addition, the zero-one laws, laws of large numbers and the central limit theorem are presented. Following this, the proof of the upper exponential bound and the statement of the Borel-Cantelli lemma which are necessary for the proof of the law of the iterated logarithm, are provided. Then, with some additional auxiliary claims, the law of the iterated logarithm is proven. At the end of the thesis, several extensions of the law of the iterated logarithm are presented and the behavior on subsequences is analysed.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:191950
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 on2024-10-30 11:50:07