Related papers: State-dependent Hawkes processes and their applica…

The self-exciting Hawkes process is widely used to model events which occur in bursts. However, many real world data sets contain missing events and/or noisily observed event times, which we refer to as data distortion. The presence of such…

We consider a sequence of systems of Hawkes processes having mean field interactions in a diffusive regime. The stochastic intensity of each process is a solution of a stochastic differential equation driven by N independent Poisson random…

In this paper we fill a gap in the literature by providing exact and explicit expressions for the correlation of general Hawkes processes together with its intensity process. Our methodology relies on the Poisson imbedding representation…

We study a linear price impact model including other liquidity takers, whose flow of orders either follows a Poisson or a Hawkes process. The optimal execution problem is solved explicitly in this context, and the closed-formula optimal…

Multivariate Hawkes processes are commonly used to model streaming networked event data in a wide variety of applications. However, it remains a challenge to extract reliable inference from complex datasets with uncertainty quantification.…

This paper presents a stochastic model motivated by the study of a virus-like evolving population with different mutation rates. This is a continuous time birth-death model: the birth processes are mutually-exciting Hawkes processes and the…

In this paper, we use the Hawkes process to model the sequence of failure, i.e., events of compressor station and conduct survival analysis on various failure events of the compressor station. However, until now, nearly all relevant…

Many fits of Hawkes processes to financial data look rather good but most of them are not statistically significant. This raises the question of what part of market dynamics this model is able to account for exactly. We document the…

The objective of this paper is to review physiological and computational aspects of the responsiveness of the cerebral cortex to stimulation, and how responsiveness depends on the state of the system. This correspondence between brain state…

We study continuous variable coherence of phase-dependent squeezed state based on an extended Hanbury Brown-Twiss scheme. High-order coherence is continuously varied by adjusting squeezing parameter $r$, displacement $\alpha $, and…

We propose a microstructural model for the order flow in financial markets that distinguishes between {\it core orders} and {\it reaction flow}, both modeled as Hawkes processes. This model has a natural scaling limit that reconciles a…

As an extension of self-exciting Hawkes process, the multivariate Hawkes process models counting processes of different types of random events with mutual excitement. In this paper, we present a perfect sampling algorithm that can generate…

Both Hawkes processes and autoregressive processes rely on linear functionals of their past, while modeling different types of data. Since datasets arising from observations of the same phenomenon may be heterogeneous and sampled at…

We extend the unstructured homogeneously mixing epidemic model introduced by Lamprinakou et al. [arXiv:2208.07340] considering a finite population stratified by age bands. We model the actual unobserved infections using a latent marked…

It is often assumed that events cannot occur simultaneously when modelling data with point processes. This raises a problem as real-world data often contains synchronous observations due to aggregation or rounding, resulting from…

We develop and apply an approach for analyzing multi-curve data where each curve is driven by a latent state process. The state at any particular point determines a smooth function, forcing the individual curve to switch from one function…

We consider oscillatory systems of interacting Hawkes processes introduced in Ditlevsen and Loecherbach (2017) to model multi-class systems of interacting neurons together with the diffusion approximations of their intensity processes. This…

We introduce a Cox-type model for relative intensities of orders flows in a limit order book. The model assumes that all intensities share a common baseline intensity, which may for example represent the global market activity. Parameters…

We propose a novel probabilistic framework to model continuous-time interaction events data. Our goal is to infer the \emph{implicit} community structure underlying the temporal interactions among entities, and also to exploit how the…

The Hawkes process (HP) is commonly used to model event sequences with self-reinforcing dynamics, including electronic health records (EHRs). Traditional HPs capture self-reinforcement via parametric impact functions that can be inspected…