Teoremi reprezentacije martingala s diskretnim vremenom

master's thesis

• Author: Marija Vukić
• Mentor: Vjekoslav Kovač (mentor)
• Committee member: Lavoslav Čaklović (predsjednik povjerenstva)
• Committee member: Igor Pažanin (član povjerenstva)
• Committee member: Marko Tadić (član povjerenstva)
• Committee member: Siniša Slijepčević (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2014-09-23, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom diplomskom radu iskazani su i dokazani teoremi reprezentacije martingala s diskretnim vremenom. Glavni rezultati su jednodimenzionalni i višedimenzionalni teorem reprezentacije te apstraktni teorem reprezentacije. Dokazane su i neke od posljedica tih teorema kao sto su: diskretna Itōva formula, prikaz varijable pomoću martingalne transformacije slučajne šetnje, Hinčinova nejednakost i konvergencija martingalne transformacije.

Abstract (english)

This thesis states and proves the discrete time martingale representation theorems. The main results are one-dimensional and multidimensional representation theorems and an abstract representation theorem. We also demonstrated some of the consequences of these theorems such as: discrete Itō’s formula, representation of variables using martingale transforms of random walks, Hinčin’s inequality and the convergence of the martingale transform.

• Keywords: teoremi reprezentacije martingala s diskretnim vremenom; jednodimenzionalni teorem reprezentacije; višedimenzionalni teorem reprezentacije; apstraktni teorem reprezentacije; diskretna Itōva formula; Hinčinova nejednakost; slučajna šetnja
• Keywords (english): discrete time martingale representation theorems; one-dimensional representation theorem; multidimensional representation theorem; abstract representation theorem; discrete Itō’s formula; Hinčin’s inequality; random walks
• Language: croatian
• URN:NBN: urn:nbn:hr:217:735707
• 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: 2019-02-19 16:44:50