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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 et al. (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.

Dates et versions

hal-03887021 , version 1 (06-12-2022)

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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-03887021⟩
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