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The stability condition for Hawkes processes and their non-linear extensions usually relies on the condition that the mean intensity is a finite constant. It follows that the total endogeneity ratio needs to be strictly smaller than unity.…
We introduce a class of hybrid marked point processes, which encompasses and extends continuous-time Markov chains and Hawkes processes. While this flexible class amalgamates such existing processes, it also contains novel processes with…
A Hawkes process model with a time-varying background rate is developed for analyzing the high-frequency financial data. In our model, the logarithm of the background rate is modeled by a linear model with a relatively large number of…
A piecewise-deterministic Markov process is a stochastic process whose behavior is governed by an ordinary differential equation punctuated by random jumps occurring at random times. We focus on the nonparametric estimation problem of the…
In this paper, we propose an extension of the Hawkes process by incorporating a kernel based on the tempered Mittag-Leffler distribution. This is the generalization of the work presented in [10]. We derive analytical results for the…
We investigate the parameter recovery of Markov-switching ordinary differential processes from discrete observations, where the differential equations are nonlinear additive models. This framework has been widely applied in biological…
We characterize a Hawkes point process with kernel proportional to the probability density function of Mittag-Leffler random variables. This kernel decays as a power law with exponent $\beta +1 \in (1,2]$. Several analytical results can be…
A field theoretical framework is developed for the Hawkes self-excited point process with arbitrary memory kernels by embedding the original non-Markovian one-dimensional dynamics onto a Markovian infinite-dimensional one. The corresponding…
This paper extends the analysis of Muni Toke and Yoshida (2020) to the case of marked point processes. We consider multiple marked point processes with intensities defined by three multiplicative components, namely a common baseline…
We introduce and show the existence of a Hawkes self-exciting point process with exponentially-decreasing kernel and where parameters are time-varying. The quantity of interest is defined as the integrated parameter…
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…
In this paper we study the frequentist properties of Bayesian approaches in linear high dimensional Hawkes processes in a sparse regime where the number of interaction functions acting on each component of the Hawkes process is much smaller…
Hawkes processes have seen a number of applications in finance, due to their ability to capture event clustering behaviour typically observed in financial systems. Given a calibrated Hawkes process, of concern is the statistical fit to…
A univariate Hawkes process is a simple point process that is self-exciting and has clustering effect. The intensity of this point process is given by the sum of a baseline intensity and another term that depends on the entire past history…
In this paper we propose an overview of the recent academic literature devoted to the applications of Hawkes processes in finance. Hawkes processes constitute a particular class of multivariate point processes that has become very popular…
The Hawkes process and its extensions effectively model self-excitatory phenomena including earthquakes, viral pandemics, financial transactions, neural spike trains and the spread of memes through social networks. The usefulness of these…
Temporal point processes (TPP) are a natural tool for modeling event-based data. Among all TPP models, Hawkes processes have proven to be the most widely used, mainly due to their adequate modeling for various applications, particularly…
The Hawkes process has garnered attention in recent years for its suitability to describe the behavior of online information cascades. Here, we present a fully tractable approach to analytically describe the distribution of the number of…
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 aim of this paper is to provide a new method for the detection of either favored or avoided distances between genomic events along DNA sequences. These events are modeled by a Hawkes process. The biological problem is actually complex…