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master's thesis
Stratonovicheve stohastičke diferencijalne jednadžbe
2023. urn:nbn:hr:126:938138
Majdenić, Jelena
Josip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics

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Majdenić, J. (2023). Stratonovicheve stohastičke diferencijalne jednadžbe (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:126:938138

Majdenić, Jelena. "Stratonovicheve stohastičke diferencijalne jednadžbe." Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2023. https://urn.nsk.hr/urn:nbn:hr:126:938138

Majdenić, Jelena. "Stratonovicheve stohastičke diferencijalne jednadžbe." Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2023. https://urn.nsk.hr/urn:nbn:hr:126:938138

Majdenić, J. (2023). 'Stratonovicheve stohastičke diferencijalne jednadžbe', Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, accessed 04 May 2024, https://urn.nsk.hr/urn:nbn:hr:126:938138

Majdenić J. Stratonovicheve stohastičke diferencijalne jednadžbe [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics; 2023 [cited 2024 May 04] Available at: https://urn.nsk.hr/urn:nbn:hr:126:938138

J. Majdenić, "Stratonovicheve stohastičke diferencijalne jednadžbe", Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, Osijek, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:126:938138

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Metadata
TitleStratonovicheve stohastičke diferencijalne jednadžbe
Title (english)Stratonovich Stochastic Differential Equations
AuthorJelena Majdenić
MentorNenad Šuvak (mentor)
Committee memberIvan Papić (predsjednik povjerenstva)
Committee memberNenad Šuvak (član povjerenstva)
Committee memberDanijel Grahovac (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics
Osijek
Defense date and country2023-10-24, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Financial and Business Mathematics
Abstract
U ovom diplomskom radu proučavana je Stratonovicheva stohastička diferencijalna jednadžba. Najprije je definirano Brownovo gibanje koji je pogonski proces Stratonovicheve stohastičke diferencijalne jednadžbe i navedena su bitna svojstva tog procesa. Definirani su Itôv i Stratonovichev stohatički integral. Pokazano je da Stratonovichev stohastički integral formalno zadovoljava pravilo za derivaciju kompozicije funkcija. Navedena je formula koja povezuje Itôv i Stratonovichev stohastički integral i služi za prelazak s Itôve stohastičke diferencijalne jednadžbe na Stratonovichevu stohastičku diferencijalnu jednadžbu. Navedeni su primjeri u kojima je dan postupak rješavanja Itôve stohastičke diferencijalne jednadžbe pomoću ekvivalentne Stratonovicheve stohastičke diferencijalne jednadžbe. Izveden je Stratonovich-Taylorov razvoj koji je temelj za Milsteinovu aproksimacijsku shemu. Na kraju su navedeni primjeri u kojima se koristi Milsteinova aproksimacijska shema za simulaciju trajektorije jakog rješenja Stratonovicheve stohastičke diferencijalne jednadžbe.
Abstract (english)
This paper studies Stratonovich stochastic differential equation. First, Brownian motion is defined, which is the driving process of Stratonovich’s stochastic differential equation, and the essential properties of that process are listed. Itô’s and Stratonovich’s stochastic integrals are defined. It is shown that the Stratonovich stochastic integral formally satisfies the chain rule. A formula that connects Itô’s and Stratonovich’s stochastic integral is given and is used to transition from Itô’s stochastic differential equation to Stratonovich’s stochastic differential equation. Examples in which the procedure for solving Itô’s stochastic differential equation using the equivalent Stratonovich stochastic differential equation are given. The Stratonovich-Taylor expansion is derived, which is the basis for the Milstein approximation scheme. Finally, examples in which the Milstein approximation scheme is used to simulate the trajectory of a strong solution of the Stratonovich stochastic differential equation are given.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:938138
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 on2023-11-08 09:45:53