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LIMIT THEOREMS FOR HAWKES PROCESSES INCLUDING INHIBITION

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-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 and versions

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

Identifiers

  • HAL Id : hal-03344416 , version 1

Cite

Patrick Cattiaux, Laetitia Colombani, Manon Costa. LIMIT THEOREMS FOR HAWKES PROCESSES INCLUDING INHIBITION. 2021. ⟨hal-03344416⟩
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