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master's thesis
Itôv integral i primjene
Zagreb: University of Zagreb, Faculty of Science, 2015. urn:nbn:hr:217:987078
Kovačević, Ana
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Kovačević, A. (2015). Itôv integral i primjene (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:987078

Kovačević, Ana. "Itôv integral i primjene." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:987078

Kovačević, Ana. "Itôv integral i primjene." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:987078

Kovačević, A. (2015). 'Itôv integral i primjene', Master's thesis, University of Zagreb, Faculty of Science, accessed 03 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:987078

Kovačević A. Itôv integral i primjene [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2015 [cited 2024 November 03] Available at: https://urn.nsk.hr/urn:nbn:hr:217:987078

A. Kovačević, "Itôv integral i primjene", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2015. Available at: https://urn.nsk.hr/urn:nbn:hr:217:987078

Metadata
TitleItôv integral i primjene
AuthorAna Kovačević
MentorAnte Mimica (mentor)
Committee memberAnte Mimica (predsjednik povjerenstva)
Committee memberNikola Sarapa (član povjerenstva)
Committee memberNela Bosner (član povjerenstva)
Committee memberAndrej Dujella (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2015-07-13, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu smo konstruirali Itôv integral koji definiramo kao limes niza slučajnih varijabli. Dokazali smo analogon Newton-Leibnizove formule, tzv. Itôvu formulu. Također, dokazali smo martingalnost Itôvog integrala čime smo, uz spomenutu formulu, dobili alat za konstrukciju martingala te ispitivanje martingalnosti slučajnih varijabli. U nastavku rada, pokazali smo konformnu invarijantnost Brownovog gibanja. Odnosno, pokazali smo da preslikavanjem Brownovog gibanja po konformnoj funkciji dobivamo vremenski izmijenjeno Brownovo gibanje. Dodatno, u prvom poglavlju smo pokazali i invarijantnost Brownovog gibanja u odnosu na skaliranje (uz vremenski pomak). U zadnjem poglavlju smo dokazali Feynman-Kacovu formulu kojom smo eksplicitno izrazili rješenje jednadžbe provođenja.
Abstract (english)
In this paper we have constructed Itô integral that is defined as a limit of certain sequence of random variables. We have proved Itô formula which is analogous to Newton–Leibniz formula. Also, we have proved that Itô integral has martingale property. Combining the last two observations, we get a powerful tool for constructing martingales and inspecting whether a random variable is a martingale. Later in the thesis we have observed conformal invariance of Brownian motion. It states that, under conformal mapping, Brownian motion is mapped to another time changed Brownian motion. However, conformal invariance is not the only invariance property of Brownian motion. In the first chapter we have shown that Brownian motion is also invariant under scaling (with a time change). In the final chapter we have proved Feynman–Kac formula which gives the explicit formula of the solution to the heat equation.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:987078
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
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Created on2019-02-15 14:03:22