Rate of convergence to equilibrium of marked Hawkes processes

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Limit Theorems for Marked Hawkes Processes with Application to a Risk Model (2012, methodology): “per bound and tilting method for the lower bound. Before we proceed, let us ﬁrst state a lemma that will be used in the proof the lower bound in Theorem 1. This result can be found in Br´emaud et al. [4]. Lemma 5. [Br´emaud et al. [4]] Consider a linear marked Hawkes process with intensity λt := α+β”
Risk Processes with Non-stationary Hawkes Claims Arrivals (2010, background): “results to non-linear Hawkes processes (see Kerstan 1964 ;B remaud and Massoulie 1996; Massoulie 1998; Bremaud et al. 2002; Torrisi 2002) would be interesting.”
HAWKES PROCESSES ON LARGE NETWORKS (2016, methodology): “In order to prove Theorems 10 and 11, we will use the following central limit theorem for martingales.”
Approximate Simulation of Hawkes Processes (2006, background): “[3] (which concerns approximate simulation of a stationary marked Hawkes process with unpredictable marks).”
Renewal in Hawkes processes with self-excitation and inhibition (2018, background): “Such equations have been introduced and studied in this context by Brémaud and Massoulié [5]; see also [6], [26].”
Perfect simulation of Hawkes processes (2005, background): “[5] studied the ‘rate of installation’, i.”