Stacionarni gaussovski procesi

master's thesis

• Author: Danijela Kolarić
• Mentor: Vjekoslav Kovač (mentor)
• Committee member: Vjekoslav Kovač (predsjednik povjerenstva)
• Committee member: Vedran Krčadinac (član povjerenstva)
• Committee member: Nenad Antonić (član povjerenstva)
• Committee member: Tina Bosner (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2017-11-28, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Gaussovski proces je u potpunosti određen očekivanjem i autokovarijacijskom funkcijom. U ovom radu proučavamo stacionarne gaussovske procese s diskretnim vremenskim parametrom te njihovu kanonsku i spektralnu reprezentaciju. Također, proučavamo karakterizaciju Markovljevog svojstva za gaussovske procese pomoću kovarijacijske matrice. Konačno, u radu se izlažu i simuliraju primjeri stacionarnih gaussovskih procesa.

Abstract (english)

A Gaussian process is completely determined by its mean and autocovariance function. In this thesis we consider stationary Gaussian processes with discrete parameter and their canonical and spectral representations. Also, we discuss the Markov property of Gaussian processes, which can be characterized in terms of the covariance function. Finally, in the thesis we discuss and simulate examples of stationary Gaussian processes.

• Keywords: gaussovski proces; stacionarni gaussovski proces; Markovljevo svojstvo za gaussovske procese
• Keywords (english): Gaussian process; stationary Gaussian process; Markov property of Gaussian processes
• Language: croatian
• URN:NBN: urn:nbn:hr:217:308901
• 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: 2018-05-25 11:45:38