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Bibliographic record number: 755077

Disertation

Author: Tadić, Tvrtko
Title: Time-like graphical models
Type: doctoral thesis
Faculty: Department of Mathematics
University: University of Washington
Location: Seattle
Date: 10.03.
Year: 2015
Page: 242
Mentor: Burdzy, Krzysztof
Keywords: Stochastic processes indexed by graphs; graphical models; time-like graphs; martingales indexed by directed sets; stochastic heat equation
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.
Project / theme: 037-0372790-2799
Original language: ENG
Research fields:
Mathematics
Full paper text: 755077.uwthesis.pdf (tekst priložen 15. Ožu. 2015. u 00:58 sati)
Contrib. to CROSBI by: Tvrtko Tadić (tvrtko.tadic@math.hr), 12. Ožu. 2015. u 22:07 sati



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