Blackwellov teorem obnavljanja

master's thesis

• Author: Barbara Banić
• Mentor: Bojan Basrak (mentor)
• Committee member: Bojan Basrak (predsjednik povjerenstva)
• Committee member: Miljenko Huzak (član povjerenstva)
• Committee member: Siniša Slijepčević (član povjerenstva)
• Committee member: Hrvoje Šikić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2019-09-23, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Cilj ovog rada je bio navesti neke osnovne pojmove i rezultate teorije obnavljanja te prezentirati dokaz Blackwellovog teorema obnavljanja. U prvom poglavlju smo se prisjetili nekih definicija i rezultata koji su korišteni u ostatku rada. U drugom poglavlju smo uveli neke osnovne pojmove i iskazali neke osnovne rezultate teorije obnavljanja. Zatim je objašnjena direktna Riemann integrabilnost te su iskazani neki uvjeti kada je ona ekvivalentna s Riemann integrabilnošću. Nakon toga smo iskazali ekvivalentne oblike teorema obnavljanja te pokazali njihovu ekvivalenciju. Na kraju smo pokazali da vrijedi Blackwellov teorem obnavljanja tako da smo prezentirali dokaz jednog od njemu ekvivalentnih oblika.

Abstract (english)

The goal of this report was to list some basic renewal theory results and present a proof of Blackwell’s renewal theorem. In the first chapter we listed some definitions and results used in the rest of the report. In the second chapter we introduced some basic renewal theory definitions and results. Next, we introduced the concept of direct Riemann integrability and conditions under which it is equivalent to Riemann integrability. After that we listed equivalent forms of renewal theorem and showed their equivalence. In the end we showed that Blackwell’s renewal theorem holds by presenting the proof of one of the equivalent forms of the renewal theorem.

• Keywords: teorija obnavljanja; Blackwellov teorem obnavljanja; Riemann integrabilnost
• Keywords (english): renewal theory; Blackwell’s renewal theorem; Riemann integrability
• Language: croatian
• URN:NBN: urn:nbn:hr:217:538700
• Study programme: Title: Finance and Business Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access; Embargo expiration date: 2020-07-09
• Created on: 2020-01-09 12:26:54