Naslov
Time-like graphical models

Autori
Tadić, Tvrtko

Vrsta, podvrsta i kategorija rada
Ocjenski radovi, doktorska disertacija

Fakultet
Department of Mathematics

Mjesto
Seattle

Datum
10.03

Godina
2015

Stranica
242

Mentor
Burdzy, Krzysztof

Ključne riječi
Stochastic processes indexed by graphs ; graphical models ; time-like graphs ; martingales indexed by directed sets ; stochastic heat equation

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA