The fundamental martingale with applications to Markov Random Fields
Probability
2024-05-15 v1
Abstract
We consider collections of SDEs indexed by a graph. Each SDE is driven by an additive Gaussian noise and each drift term interacts with all other SDEs within the graph neighbourhood. We derive the fundamental martingale for a class of Gaussian processes and use this to prove a Girsanov type theorem. Further, we use this to construct a clique factorisation to prove that the law of the interacting SDEs forms a 2-Markov Random Field.
Keywords
Cite
@article{arxiv.2405.08795,
title = {The fundamental martingale with applications to Markov Random Fields},
author = {Kevin Hu and Kavita Ramanan and William Salkeld},
journal= {arXiv preprint arXiv:2405.08795},
year = {2024}
}