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master's thesis
Egzaktna simulacija trajektorija difuzija
Zagreb: University of Zagreb, Faculty of Science, 2023. urn:nbn:hr:217:856220
Knežević, Marin
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Knežević, M. (2023). Egzaktna simulacija trajektorija difuzija (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:856220

Knežević, Marin. "Egzaktna simulacija trajektorija difuzija." Master's thesis, University of Zagreb, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:217:856220

Knežević, Marin. "Egzaktna simulacija trajektorija difuzija." Master's thesis, University of Zagreb, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:217:856220

Knežević, M. (2023). 'Egzaktna simulacija trajektorija difuzija', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 May 2024, https://urn.nsk.hr/urn:nbn:hr:217:856220

Knežević M. Egzaktna simulacija trajektorija difuzija [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2023 [cited 2024 May 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:856220

M. Knežević, "Egzaktna simulacija trajektorija difuzija", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:217:856220

Metadata
TitleEgzaktna simulacija trajektorija difuzija
Title (english)Exact simulation of diffusion trajectories
AuthorMarin Knežević
MentorVanja Wagner (mentor)
Committee memberVanja Wagner (predsjednik povjerenstva)
Committee memberSnježana Lubura Strunjak (član povjerenstva)
Committee memberDražen Adamović (član povjerenstva)
Committee memberMarko Tadić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2023-03-03, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovome radu proučavamo metode simulacija trajektorija difuzija određenih stohastičkim diferencijalnim jednadžbama s posebnim naglaskom na egzaktnu metodu koja se temelji na uzorkovanju s odbacivanjem. U prvom poglavlju dajemo pregled teorije slučajnih procesa i Itovog diferencijalnog računa potrebnog za sva daljnja razmatranja. U drugom poglavlju predstavljamo klasičnu metodu prihvaćanja i odbacivanja odnosno “rejection sampling” uvodeći pritom i alternativan pristup korišten u egzaktnoj metodi. Nadalje, u trećem poglavlju iz teoretske perspektive prezentiramo metode za simulaciju trajektorija difuzija, prvo Eulerovu metodu i zatim egzaktnu metodu. Također, dajemo ocjenu efikasnosti egzaktnog algoritma. Konačno, u četvrtom poglavlju obje metode implementiramo u matematičkom programskom okruženju R te vršimo usporedbe na konkretnoj stohastičkoj diferencijalnoj jednadžbi.
Abstract (english)
In this thesis, we study different methods of simulating diffusion trajectories determined by stochastic differential equations with special emphasis on the exact method based on rejection sampling. In the first chapter, we give an overview of the theory behind stochastic processes and Ito's differential calculus necessary for all further considerations. In the second chapter, we present the standard method of rejection sampling, while also introducing an alternative approach used in the exact method. Furthermore, in the third chapter, from a theoretical perspective, we present methods for simulating diffusion trajectories, first the Euler method and then the exact method. We also evaluate the efficiency of the exact algorithm. Finally, in the fourth chapter, we implement both methods using the mathematical programming environment R and perform comparisons given a fixed stochastic differential equation.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:856220
Study programmeTitle: Finance and Business 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 on2023-07-26 08:47:05