The rescaled marked Hawkes point measure with immigration converges to a Gaussian white noise plus a Brownian-motion lifting, and the shot noise converges to a Brownian martingale.
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Functional Limit Theorems for Marked Hawkes Point Measures
The rescaled marked Hawkes point measure with immigration converges to a Gaussian white noise plus a Brownian-motion lifting, and the shot noise converges to a Brownian martingale.