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Article Dans Une Revue Stochastic Processes and their Applications Année : 2022

LIMIT THEOREMS FOR HAWKES PROCESSES INCLUDING INHIBITION

Résumé

In this paper we consider some non linear Hawkes processes with signed reproduction function (or memory kernel) thus exhibiting both self-excitation and inhibition. We provide a Law of Large Numbers, a Central Limit Theorem and large deviation results, as time growths to infinity. The proofs lie on a renewal structure for these processes introduced in Costa-Graham-Marsalle-Tran (2020) which leads to a comparison with cumulative processes. Explicit computations are made on some examples. Similar results have been obtained in the literature for self-exciting Hawkes processes only.
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Dates et versions

hal-03344416 , version 1 (15-09-2021)

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Patrick Cattiaux, Laetitia Colombani, Manon Costa. LIMIT THEOREMS FOR HAWKES PROCESSES INCLUDING INHIBITION. Stochastic Processes and their Applications, 2022, 149, pp.404-426. ⟨10.1016/j.spa.2022.04.002⟩. ⟨hal-03344416⟩
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