Limit theorems for Hawkes processes including inhibition

Patrick Cattiaux, Laetitia Colombani and Manon Costa

Stochastic Processes and their Applications, 2022, vol. 149, issue C, 404-426

Abstract: 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.

Keywords: Hawkes processes; Inhibition; Renewal theory; Limit theorems (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spa.2022.04.002

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