The fundamental martingale with applications to Markov Random Fields

Kevin Hu; Kavita Ramanan; William Salkeld

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arXiv · 2405.08795

The fundamental martingale with applications to Markov Random Fields

Kevin Hu·Kavita Ramanan·William Salkeld

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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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Kevin Hu, Kavita Ramanan, William Salkeld. 2024-05-14. The fundamental martingale with applications to Markov Random Fields. https://arxiv.org/abs/2405.08795

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