Some limit theorems for locally stationary Hawkes processes

Fuente: arXiv
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Autori principali: Deschatre, Thomas, Gruet, Pierre, Lotz, Antoine
Natura: Preprint
Pubblicazione: 2025
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author Deschatre, Thomas
Gruet, Pierre
Lotz, Antoine
author_facet Deschatre, Thomas
Gruet, Pierre
Lotz, Antoine
contents We prove a law of large numbers and functional central limit theorem for a class of multivariate Hawkes processes with time-dependent reproduction rate. We address the difficulties induced by the use of non-convolutive Volterra processes by recombining classical martingale methods introduced in Bacry et al. [3] with novel ideas proposed by Kwan et al. [19]. The asymptotic theory we obtain yields useful applications in financial statistics. As an illustration, we derive closed-form expressions for price distortions under liquidity constraints.
format Preprint
id arxiv_https___arxiv_org_abs_2501_17245
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Some limit theorems for locally stationary Hawkes processes
Deschatre, Thomas
Gruet, Pierre
Lotz, Antoine
Probability
60F05, 60G55, 62M10, 62P05
We prove a law of large numbers and functional central limit theorem for a class of multivariate Hawkes processes with time-dependent reproduction rate. We address the difficulties induced by the use of non-convolutive Volterra processes by recombining classical martingale methods introduced in Bacry et al. [3] with novel ideas proposed by Kwan et al. [19]. The asymptotic theory we obtain yields useful applications in financial statistics. As an illustration, we derive closed-form expressions for price distortions under liquidity constraints.
title Some limit theorems for locally stationary Hawkes processes
topic Probability
60F05, 60G55, 62M10, 62P05
url https://arxiv.org/abs/2501.17245