Nearly unstable Hawkes processes rescale to affine stochastic Volterra diffusions, and mean-field Hawkes systems exhibit synchronization, conditional independence, or extinction depending on n(1-||phi^n||)^2.
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Mean-Field Limits for Nearly Unstable Hawkes Processes
Nearly unstable Hawkes processes rescale to affine stochastic Volterra diffusions, and mean-field Hawkes systems exhibit synchronization, conditional independence, or extinction depending on n(1-||phi^n||)^2.