Ergodski teorem i stacionarni procesi

master's thesis

• Author: Ema Šimon
• Mentor: Ante Mimica (mentor)
• Committee member: Vjekoslav Kovač (predsjednik povjerenstva)
• Committee member: Damir Bakić (član povjerenstva)
• Committee member: Miljenko Huzak (član povjerenstva)
• Committee member: Pavle Goldstein (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2016-09-27, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Ovaj diplomski rad se bavi klasičnim Birkhoff-Hinčinovim ergodskim teoremom te teorijom potrebnom za njegov dokaz. Uz to, uvodi se pojam ergodskog stacionarnog slučajnog procesa te se dokazuje ergodski teorem za takve procese. Na kraju se dokazuje subaditivan ergodski teorem koji je poopćenje oba prethodno navedena rezultata te se daju primjeri korištenja ergodskih teorema.

Abstract (english)

In this graduate thesis we are examining the classical Birkhoff-Hinčin ergodic theorem and the mathematical framework surrounding it. We are also defining ergodic stationary processes and giving the proof for the version of the ergodic theorem concerning those processes. Subadditive ergodic theorem, which is a generalization of the previously mentioned theorems, is given along with its proof and the applications of ergodic theorems are shown on several examples.

• Keywords: klasični Birkhoff-Hinčinov ergodski teorem; ergodski stacionarni slučajni proces; subaditivan ergodski teorem
• Keywords (english): classical Birkhoff-Hinčin ergodic theorem; ergodic stationary processes; subadditive ergodic theorem
• Language: croatian
• URN:NBN: urn:nbn:hr:217:120302
• Study programme: Title: Mathematical Statistics; 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
• Created on: 2019-02-13 11:40:21