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Teoremi reprezentacije martingala s diskretnim vremenom

By Marija Vukić

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.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

Topics: teoremi reprezentacije martingala s diskretnim vremenom, jednodimenzionalni teorem reprezentacije, višedimenzionalni teorem reprezentacije, apstraktni teorem reprezentacije, diskretna Itōva formula, Hinčinova nejednakost, slučajna šetnja, discrete time martingale representation theorems, one-dimensional representation theorem, multidimensional representation theorem, abstract representation theorem, discrete Itō’s formula, Hinčin’s inequality, random walks, PRIRODNE ZNANOSTI. Matematika., NATURAL SCIENCES. Mathematics.
Publisher: University of Zagreb. Faculty of Science. Department of Mathematics.
Year: 2014
OAI identifier: oai:repozitorij.unizg.hr:pmf_5587

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