For interacting jump processes whose single-particle transitions form an acyclic graph, the hydrodynamic limit of the neighborhood empirical measure equals the solution of a finite ODE system, the Markov local-field forward equations.
Agathe-Nerine, Multivariate hawkes processes on inhomogeneous random graphs, Stochastic Processes and their Applications 152 (2022), 86–148
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Tractable description of hydrodynamic limits of a class of interacting jump processes on sparse graphs
For interacting jump processes whose single-particle transitions form an acyclic graph, the hydrodynamic limit of the neighborhood empirical measure equals the solution of a finite ODE system, the Markov local-field forward equations.