prikaz prve stranice dokumenta Elements of renewal theory for cluster point processes
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doctoral thesis
Elements of renewal theory for cluster point processes
Zagreb: University of Zagreb, Faculty of Science, 2022. urn:nbn:hr:217:954378
Dajaković, Marina
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Dajaković, M. (2022). Elements of renewal theory for cluster point processes (Doctoral thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:954378

Dajaković, Marina. "Elements of renewal theory for cluster point processes." Doctoral thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:954378

Dajaković, Marina. "Elements of renewal theory for cluster point processes." Doctoral thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:954378

Dajaković, M. (2022). 'Elements of renewal theory for cluster point processes', Doctoral thesis, University of Zagreb, Faculty of Science, accessed 26 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:954378

Dajaković M. Elements of renewal theory for cluster point processes [Doctoral thesis]. Zagreb: University of Zagreb, Faculty of Science; 2022 [cited 2024 November 26] Available at: https://urn.nsk.hr/urn:nbn:hr:217:954378

M. Dajaković, "Elements of renewal theory for cluster point processes", Doctoral thesis, University of Zagreb, Faculty of Science, Zagreb, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:217:954378

Metadata
TitleElements of renewal theory for cluster point processes
Title (croatian)Elementi teorije obnavljanja za točkovne procese s klasterima
AuthorMarina Dajaković
MentorBojan Basrak (mentor)
Committee memberNikola Sandrić (predsjednik povjerenstva)
Committee memberHrvoje Planinić (član povjerenstva)
Committee memberAlexander Marynych https://orcid.org/0000-0002-7628-7541 (član povjerenstva)
Committee memberBojan Basrak (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2022-11-10, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Universal decimal classification
(UDC)		51 - Mathematics
Abstract
The main goal of this thesis is to discuss renewal theorems in the framework of the cluster point processes on the real line. More precisely, under appropriate integrability assumptions, we describe the asymptotic distribution of the shifted renewal cluster point process and, as a consequence, we show that its mean measure on a bounded interval is asymptotically proportional to the length of the interval. Also, we prove the equivalent version of the latter result that allows one to determine the asymptotic behavior of the functions of special convolution form. These generalizations of the well-known results from the standard renewal theory are obtained using the methods and tools of modern probability theory, such as point process theory, especially vague convergence, and coupling method.
Abstract (croatian)
Glavni cilj ove disertacije je diskutirati teoreme obnavljanja u kontekstu točkovnih procesa s klasterima na skupu realnih brojeva. Preciznije, uz određene pretpostavke na prve momente, opisujemo asimptotsku distribuciju pomaknutog točkovnog procesa s klasterima te, kao posljedicu, pokazujemo da je srednja mjera takvog procesa na ograničenom intervalu proporcionalna duljini intervala. Također, dokazujemo ekvivalentnu verziju prethodnog rezultata koja omogućuje određivanje asimptotskog ponašanja konvolucije funkcija specijalnog oblika. Navedene generalizacije dobro poznatih rezultata iz standardne teorije obnavljanja su dobivene korištenjem metoda i alata moderne teorije vjerojatnosti, kao što su teorija točkovnih procesa, posebno vague konvergencija, te metoda sparivanja.
Keywords
Keywords (croatian)
Languageenglish
URN:NBNurn:nbn:hr:217:954378
Study programmeTitle: Mathematics
Study programme type: university
Study level: postgraduate
Academic / professional title: doktor/doktorica znanosti, područje prirodnih znanosti, polje matematika (doktor/doktorica znanosti, područje prirodnih znanosti, polje matematika)
Type of resourceText
Extentviii, 79 str.
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2023-03-01 13:45:50