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master's thesis
Slučajni procesi definirani integralom u odnosu na slučajnu mjeru
2022. urn:nbn:hr:126:434654
Mihalčić, Dominik
Josip Juraj Strossmayer University of Osijek
Department of Mathematics

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Mihalčić, D. (2022). Slučajni procesi definirani integralom u odnosu na slučajnu mjeru (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:434654

Mihalčić, Dominik. "Slučajni procesi definirani integralom u odnosu na slučajnu mjeru." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2022. https://urn.nsk.hr/urn:nbn:hr:126:434654

Mihalčić, Dominik. "Slučajni procesi definirani integralom u odnosu na slučajnu mjeru." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2022. https://urn.nsk.hr/urn:nbn:hr:126:434654

Mihalčić, D. (2022). 'Slučajni procesi definirani integralom u odnosu na slučajnu mjeru', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 22 January 2025, https://urn.nsk.hr/urn:nbn:hr:126:434654

Mihalčić D. Slučajni procesi definirani integralom u odnosu na slučajnu mjeru [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2022 [cited 2025 January 22] Available at: https://urn.nsk.hr/urn:nbn:hr:126:434654

D. Mihalčić, "Slučajni procesi definirani integralom u odnosu na slučajnu mjeru", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:126:434654

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Metadata
TitleSlučajni procesi definirani integralom u odnosu na slučajnu mjeru
Title (english)Stochastic Processes Defined by the Integral with Respect to a Random Measure
AuthorDominik Mihalčić
MentorDanijel Grahovac (mentor)
Committee memberNenad Šuvak (predsjednik povjerenstva)
Committee memberDanijel Grahovac (član povjerenstva)
Committee memberIvan Papić (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Osijek
Defense date and country2022-09-28, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Probability Theory and Statistics
Abstract
U ovom radu najprije je objašnjen pojam beskonačne djeljivosti za slučajne varijable, vektore i procese. Kao poseban oblik slučajnog procesa, definirana je slučajna mjera. Izvedeni su različiti oblici njezine karakteristične funkcije te su dani najvažniji primjeri slučajnih mjera. Integral u odnosu na slučajnu mjeru najprije je definiran za jednostavne, a potom za općenite funkcije. Navedeni su nužni i dovoljni uvjeti na podintegralnu funkciju koji osiguravaju da je integral dobro definiran. Izvedeni su eksplicitni izrazi za karakterističnu trojku beskonačno djeljive slučajne varijable definirane integralom. Pokazano je da je familija integrala u odnosu na beskonačno djeljivu slučajnu mjeru beskonačno djeljiv slučajni proces. Navedeni su primjeri procesa definiranih integralom i njihova najvažnija svojstva. Diskutirani su stacionarni i sebi slični procesi te je komentirana struktura njihove zavisnosti.
Abstract (english)
This paper firstly explains the concept of infinite divisibility for random variables, vectors and processes. As a special case of random process, a random measure is defined. Different forms of its characteristic function were derived and the most important examples of random measures were given. Integral with respect to a random measure is defined first for simple and then for general functions. The necessary and sufficient conditions for the integrand are specified which ensure that the integral is well defined. Explicit expressions were derived for the characteristic triple of an infinitely divisible random variable defined by the integral. It has been shown that the family of integrals with respect to an infinitely divisible random measure is an infinitely divisible random process. Examples of processes defined by integral are given with their most important properties. Stationary and self-similar processes were discussed and the structure of their dependency was commented on.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:434654
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 on2022-09-29 06:23:29