Time-like graphical models
Abstract
We study continuous processes indexed by a special family of graphs. Processes indexed by vertices of graphs are known as probabilistic graphical models. Burdzy and Pal in their paper proposed a continuous version of graphical models -- processes indexed by time-like graphs. We construct a more general family of continuous processes on a wider family of graphs, find new properties and solve the conjecture of uniqueness of the distribution for the process indexed by graphs with infinite number of vertices. We present new results showing connections to the stochastic heat equation, Markov random fields, martingales indexed by directed sets and branching Markov processes.
Cite
@article{arxiv.1311.6193,
title = {Time-like graphical models},
author = {Tvrtko Tadić},
journal= {arXiv preprint arXiv:1311.6193},
year = {2016}
}
Comments
146 pages. Typos removed and some technical problems resolved. To appear in Memoirs of the American Mathematical Society