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master's thesis
Sebi - slični procesi
Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. urn:nbn:hr:126:664357
Ćurić, Mia
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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Ćurić, M. (2019). Sebi - slični procesi (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:664357

Ćurić, Mia. "Sebi - slični procesi." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:664357

Ćurić, Mia. "Sebi - slični procesi." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:664357

Ćurić, M. (2019). 'Sebi - slični procesi', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 25 September 2023, https://urn.nsk.hr/urn:nbn:hr:126:664357

Ćurić M. Sebi - slični procesi [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2019 [cited 2023 September 25] Available at: https://urn.nsk.hr/urn:nbn:hr:126:664357

M. Ćurić, "Sebi - slični procesi", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:126:664357

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Metadata
TitleSebi - slični procesi
Title (english)Self - Similar Processes
AuthorMia Ćurić
MentorDanijel Grahovac (mentor)
Committee memberMirta Benšić (predsjednik povjerenstva)
Committee memberDanijel Grahovac (član povjerenstva)
Committee memberDragana Jankov Maširević (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 country2019-09-06, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Probability Theory and Statistics
Abstract
U ovom diplomskom radu predstavljeni su sebi-slični procesi, njihova definicija i svojstva koja su direktna posljedica sebi-sličnosti. Opisana je veza sebi-sličnih procesa i strogo stacionarnih procesa te je dokazan Lampertijev fundamentalni granični teorem. Nadalje, dani su primjeri sebi-sličnih procesa, kao što su Brownovo gibanje, stabilni Levyjevi procesi te frakcionalno Brownovo gibanje. Proučen je frakcionalni Gaussovski šum, koji je stacionaran niz prirasta frakcionalnog Brownovog gibanja. Simulirane su trajektorije frakcionalnog Gaussovskog šuma za različite vrijednosti parametra sebi-sličnosti. Zatim je proučena klasa sebi-sličnih procesa sa stacionarnim prirastima, koji nisu nužno Gaussovski. Promatran je slučaj sebi-sličnih procesa s konačnom varijancom, te posebno Hermitov proces. Opisani su stabilni sebi-slični procesi sa stacionarnim prirastima, te linearno frakcionalno stabilno gibanje kao primjer takvih procesa.
Abstract (english)
In this graduate thesis, self-similar processes, their definition and properties which are direct result of self-similarity, are presented. The connection of self-similar processes and strictly stationary processes is described and Lamperti’s fundamental limit theorem is proved. Furthermore, examples of self-similar processes, such as Brownian motion, stable Levy processes and fractional Brownian motion, are given. Fractional Gaussian noise, which is stationary sequence of increments of fractional Brownian motion, is studied. Sample paths of fractional Gaussian noise are simulated for different value of self-similarity parameter. Then, class of self-similar processes with stationary increments, which are not necessarily Gaussian, is studied. Next, the self-similar processes with the finite variance are studied, in particular Hermite processes. Stable self-similar processes with stationary increments are described, and linear fractional stable motion is given as example.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:664357
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
RepositoryRepository of School of Applied Mathematics and Computer Science
Created on2019-09-09 08:51:42