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Related papers: Hawkes process with tempered Mittag-Leffler kernel

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The Hawkes process is a class of point processes whose future depends on their own history. Previous theoretical work on the Hawkes process is limited to a special case in which a past event can only increase the occurrence of future…

Methodology · Statistics 2019-06-21 Shizhe Chen , Ali Shojaie , Eric Shea-Brown , Daniela Witten

The Hawks process is a point process with a self-exciting property. It has been used to model earthquakes, social media events, infections, etc., and is getting a lot of attention. However, as a real problem, there are often situations…

Statistics Theory · Mathematics 2021-07-30 Masatoshi Goda

In classical Hawkes process, the baseline intensity and triggering kernel are assumed to be a constant and parametric function respectively, which limits the model flexibility. To generalize it, we present a fully Bayesian nonparametric…

Machine Learning · Computer Science 2019-10-30 Feng Zhou , Zhidong Li , Xuhui Fan , Yang Wang , Arcot Sowmya , Fang Chen

Classic estimation methods for Hawkes processes rely on the assumption that observed event times are indeed a realisation of a Hawkes process, without considering any potential perturbation of the model. However, in practice, observations…

Methodology · Statistics 2025-08-21 Anna Bonnet , Felix Cheysson , Miguel Martinez Herrera , Maxime Sangnier

We establish the asymptotic validity of frequency-domain inference for stationary multivariate Hawkes processes under mild conditions, bridging the gap between theory and application. By developing upper-bounds on the reduced cumulant…

Statistics Theory · Mathematics 2026-04-14 Yifu Tang , Conor Kresin , Boris Baeumer , Ting Wang

We study statistical aspects of state-dependent Hawkes processes, which are an extension of Hawkes processes where a self- and cross-exciting counting process and a state process are fully coupled, interacting with each other. The…

Statistical Finance · Quantitative Finance 2021-09-17 Maxime Morariu-Patrichi , Mikko S. Pakkanen

Hawkes processes are a class of point processes that have the ability to model the self- and mutual-exciting phenomena. Although the classic Hawkes processes cover a wide range of applications, their expressive ability is limited due to…

Machine Learning · Computer Science 2021-06-10 Feng Zhou , Quyu Kong , Yixuan Zhang , Cheng Feng , Jun Zhu

This study explores the application of Hawkes processes to model high-frequency data in the context of limit order books. Two distinct Hawkes-based models are proposed and analyzed: one utilizing exponential kernels and the other employing…

Mathematical Finance · Quantitative Finance 2025-03-20 Neal Batra

In this paper, we develop an efficient nonparametric Bayesian estimation of the kernel function of Hawkes processes. The non-parametric Bayesian approach is important because it provides flexible Hawkes kernels and quantifies their…

Machine Learning · Computer Science 2022-04-14 Rui Zhang , Christian Walder , Marian-Andrei Rizoiu , Lexing Xie

Event-driven systems in fields such as neuroscience, social networks, and finance often exhibit dynamics influenced by continuously evolving external covariates. Motivated by these applications, we introduce a new class of multivariate…

Statistics Theory · Mathematics 2025-12-02 Maya Sadeler Perrin , Anna Bonnet , Charlotte Dion-Blanc , Adeline Samson

Hawkes Processes are a type of point process for modeling self-excitation, i.e., when the occurrence of an event makes future events more likely to occur. The corresponding self-triggering function of this type of process may be inferred…

Applications · Statistics 2018-06-01 Rafael Lima , Jaesik Choi

We introduce the Hyperedge-triggered Hawkes (HTH) process for inferring higher-order interaction structure in multi-cellular systems from asynchronous event-time data. Beyond standard pairwise excitation, the HTH intensity includes a term…

Methodology · Statistics 2026-05-27 Zihan Xu

We study large time behavior of critical marked Hawkes processes and related branching particle systems. In case of marked Hawkes processes we assume that the kernel function has multiplicative form and the marks corresponding to the events…

Probability · Mathematics 2026-05-05 Anna Talarczyk

Hawkes processes have recently gained increasing attention from the machine learning community for their versatility in modeling event sequence data. While they have a rich history going back decades, some of their properties, such as…

The Hawkes process (HP) has been widely applied to modeling self-exciting events including neuron spikes, earthquakes and tweets. To avoid designing parametric triggering kernel and to be able to quantify the prediction confidence, the…

Machine Learning · Computer Science 2021-02-05 Rui Zhang , Christian Walder , Marian-Andrei Rizoiu

The multivariate Hawkes process is a past-dependent point process used to model the relationship of event occurrences between different phenomena.Although the Hawkes process was originally introduced to describe excitation effects, which…

Methodology · Statistics 2023-06-30 Anna Bonnet , Miguel Martinez Herrera , Maxime Sangnier

Recently proposed encoder-decoder structures for modeling Hawkes processes use transformer-inspired architectures, which encode the history of events via embeddings and self-attention mechanisms. These models deliver better prediction and…

Machine Learning · Computer Science 2022-02-07 Yamac Alican Isik , Connor Davis , Paidamoyo Chapfuwa , Ricardo Henao

We design a new nonparametric method that allows one to estimate the matrix of integrated kernels of a multivariate Hawkes process. This matrix not only encodes the mutual influences of each nodes of the process, but also disentangles the…

Machine Learning · Statistics 2017-05-31 Massil Achab , Emmanuel Bacry , Stéphane Gaïffas , Iacopo Mastromatteo , Jean-Francois Muzy

We present a modified version of the non parametric Hawkes kernel estimation procedure studied in arXiv:1401.0903 that is adapted to slowly decreasing kernels. We show on numerical simulations involving a reasonable number of events that…

Statistical Finance · Quantitative Finance 2014-12-30 Emmanuel Bacry , Thibault Jaisson , Jean-Francois Muzy

Existence and stability properties are studied for Hawkes process, i.e. point process $S$ that has long-memory and intensity $r(t)=\lambda \big(g_0(t)+ \sum_{\tau<t, \tau \in S} h(t-\tau) \big)$. The approach to Hawkes process presented in…

Probability · Mathematics 2013-01-17 Dmytro Karabash