prikaz prve stranice dokumenta Lévyjev let
  Download
PDF 1.72 MB
master's thesis
Lévyjev let
Zagreb: University of Zagreb, Faculty of Science, 2018. urn:nbn:hr:217:669463
Marić, Dejan
University of Zagreb
Faculty of Science
Department of Physics

Institutional repository: Repository of the Faculty of Science

Cite this document

Marić, D. (2018). Lévyjev let (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:669463

Marić, Dejan. "Lévyjev let." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:669463

Marić, Dejan. "Lévyjev let." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:669463

Marić, D. (2018). 'Lévyjev let', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:669463

Marić D. Lévyjev let [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2018 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:669463

D. Marić, "Lévyjev let", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2018. Available at: https://urn.nsk.hr/urn:nbn:hr:217:669463

Metadata
TitleLévyjev let
Title (english)Lévy flight
AuthorDejan Marić
MentorDavor Horvatić (mentor)
Committee memberDavor Horvatić (predsjednik povjerenstva)
Committee memberKrešimir Kumerički (član povjerenstva)
Committee memberŽeljko Skoko (član povjerenstva)
Committee memberMihael Makek (član povjerenstva)
Committee memberNikola Poljak (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Physics)
Zagreb
Defense date and country2018-09-27, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Physics
Abstract
U ovom radu opisani su nasumični procesi, njihova svojstva te primjena u fizici i u drugim poljima znanosti. Proces nasumičnog gibanja prvi je uočio botaničar Robert Brown. Brownovo gibanje je u skladu s centralnim graničnim teoremom koji govori kako srednja vrijednost dovoljno velikog broja nasumičnih varijabli, od kojih svaka ima konačnu varijancu, slijedi normalnu (Gaussovu) raspodjelu. Opisat ćemo i procese koji odstupaju od centralnog graničnog teorema, a jedan od takvih procesa je Lévyjev let koji opisuje nasumičan hod kod kojeg duljine koraka imaju teškorepu (eng. heavy tailed) raspodjelu, odnosno raspodjelu vjerojatnosti čiji krajevi nemaju eksponencijalni pad. Takva raspodjela vjerojatnosti ima za krajnje vrijednosti puno veće vrijednosti nego normalna raspodjela. Lévyjeva raspodjela je generalizacija normalne raspodjele za sumu nezavisnih varijabli u slučajevima kada varijance varijabli divergiraju, odnosno idu u beskonačnost. Zbog svojih svojstava, ovakvi procesi pružaju izvrstan alat za opis mnogih prirodnih fenomena u fizici i drugim znanostima, što je ilustirano kroz praktične primjere u fizici te kod dinamike bankrota.
Abstract (english)
This thesis gives an overview of random processes, their properties and their application in physics and in other fields of science. The process of the random movement was first observed by botanist Robert Brown. Brown’s motion is consistent with the central limit theorem, which states that the mean value of a sufficiently large number of random variables, each having a finite variance, follows a normal (Gauss) distribution. Processes that deviate from the central limit theorem and one such process is the Lévy flight which describes a random walk in which the length of the steps has heavy-tailed distribution, i.e. probability distribution whose ends do not have an exponential drop. Lévy distribution is the generalization of the normal distribution for the case where variance of the sum of independent variables diverges or goes to infinity. Because of its properties, Lévy distribution provides an excellent tool for describing many natural phenomena in physics and other sciences, which is illustrated through practical examples in physics and dynamics of bankruptcy.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:669463
Study programmeTitle: Physics; specializations in: Education
Course: Education
Study programme type: university
Study level: integrated undergraduate and graduate
Academic / professional title: magistar/magistra edukacije fizike (magistar/magistra edukacije fizike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2018-11-19 16:33:59