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master's thesis
Monte Carlo metode
Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. urn:nbn:hr:126:012597
Budetić, Mia
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics and Mathematics Teaching
Algebra, Analysis and Number Theory Research Group

Institutional repository: Repository of School of Applied Mathematics and Informatics

Cite this document

Budetić, M. (2020). Monte Carlo metode (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:012597

Budetić, Mia. "Monte Carlo metode." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. https://urn.nsk.hr/urn:nbn:hr:126:012597

Budetić, Mia. "Monte Carlo metode." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. https://urn.nsk.hr/urn:nbn:hr:126:012597

Budetić, M. (2020). 'Monte Carlo metode', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 25 January 2025, https://urn.nsk.hr/urn:nbn:hr:126:012597

Budetić M. Monte Carlo metode [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2020 [cited 2025 January 25] Available at: https://urn.nsk.hr/urn:nbn:hr:126:012597

M. Budetić, "Monte Carlo metode", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:126:012597

Metadata
TitleMonte Carlo metode
Title (english)Monte Carlo Methods
AuthorMia Budetić
MentorMirta Benšić (mentor)
Committee memberNenad Šuvak (predsjednik povjerenstva)
Committee memberIvan Soldo (član povjerenstva)
Committee memberDanijel Grahovac (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Pure Mathematics and Mathematics Teaching)
(Algebra, Analysis and Number Theory Research Group)
Osijek
Defense date and country2020-11-27, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Probability Theory and Statistics
Abstract
Monte Carlo metode su bilo koji matematički modeli i algoritmi čija je glavna značajka korištenje velikog broja slučajnih brojeva koji se simuliraju nasumičnim uzorkovanjem. Izuzetno su prikladne za rješavanje širokog spektra složenih problema u različitim poljima znanosti. U prvom dijelu rada opisani su načini generiranja realizacija nizova nezavisnih slučajnih varijabli, čija se kvaliteta ispituje statističkim testovima. Drugim dijelom dan je uvid u dvije različite metode generiranja realizacija slučajnih varijabli, metode inverzije i metode odbacivanja. Nakon toga, s ciljem procjene matematičkih izraza poput konačnih integrala, objašnjena je metoda Monte Carlo integracije. Na kraju je opisana tehnika redukcije varijance uzorkovanja po važnosti kojom se procjenjuju rijetki događaji.
Abstract (english)
Monte Carlo methods are any mathematical models and algorithms whose main feature is the usage of large number of random numbers that are simulated by random sampling. They are extremely suitable for solving a wide range of complex problems in various fields of science. The first part of the paper describes the ways of generating the realization of a series of independent random variables, the quality of which is examined by statistical tests. The second part provides an insight into two different methods of generating the realization of random variables, the inversion method and the rejection method. Subsequently, in order to estimate mathematical expressions such as finite integrals, the Monte Carlo integration method is explained. Finally, variance reduction technique called importance sampling used for estimating rare events is described.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:012597
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 on2020-11-30 08:12:00