Time-like graphical models

doctoral thesis

• Author: Tvrtko Tadić
• Mentor: Krzysztof Burdzy (mentor); VIAF: 109558458
• Committee member: Krzysztof Burdzy (predsjednik povjerenstva); VIAF: 109558458
• Committee member: Zhen-Qing Chen (član povjerenstva); VIAF: 219986120
• Committee member: Soumik Pal (član povjerenstva); strani drzavljanin: Nije dostupno
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Granter: United States: University of Washington; Seattle
• Defense date and country: 2015-03-10, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics
• Universal decimal classification (UDC): 51 - Mathematics

Abstract

We study continuous processes indexed by a special family of graphs. Processes indexed by vertices of graphs are known as probabilistic graphical models. In 2011, Burdzy and Pal proposed a continuous version of graphical models indexed by graphs with an embedded time structure -- so called time-like graphs. We extend the notion of time-like graphs and find properties of processes indexed by them. In particular, we solve the conjecture of uniqueness of the distribution for the process indexed by graphs with infinite number of vertices. We provide a new result showing the stochastic heat equation as a limit of the sequence of natural Brownian motions on time-like graphs. In addition, our treatment of time-like graphical models reveals connections to Markov random fields, martingales indexed by directed sets and branching Markov processes.

Abstract (croatian)

Rad ne sadrži sažetak na drugom jeziku.

• Keywords: stochastic processes indexed by graphs; graphical models; time-like graphs; martingales indexed by directed sets; stochastic heat equation
• Keywords (croatian): Rad ne sadrži ključne riječi na drugom jeziku.
• Language: english
• URN:NBN: urn:nbn:hr:217:779202
• Study programme: Title: Mathematics; Study programme type: university; Study level: postgraduate; Academic / professional title: doktor/doktorica znanosti, područje prirodnih znanosti, polje matematika (doktor/doktorica znanosti, područje prirodnih znanosti, polje matematika)
• Type of resource: Text
• Extent: vii, 235 str.
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-03-26 13:23:05