May 14, 2024Open Access

The fundamental martingale with applications to Markov Random Fields

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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.

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Hu et al. (Tue,) studied this question.

synapsesocial.com/papers/68e6a4e2b6db643587627b98 https://doi.org/https://doi.org/10.48550/arxiv.2405.08795

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