A subcriticality criterion β_*/(β^* - β_*) > 1 guarantees almost-sure finiteness of the clan of ancestors, enabling an exact backward-forward perfect simulation algorithm for the stationary regime of these variable-memory Hawkes processes.
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Perfect simulation for interacting Hawkes processes with reset-induced variable length memory
A subcriticality criterion β_*/(β^* - β_*) > 1 guarantees almost-sure finiteness of the clan of ancestors, enabling an exact backward-forward perfect simulation algorithm for the stationary regime of these variable-memory Hawkes processes.