Related papers: Large deviations and applications for Markovian Ha…
The Hawkes model is suitable for describing self and mutually exciting random events. In addition, the exponential decay in the Hawkes process allows us to calculate the moment properties in the model. However, due to the complexity of the…
This paper introduces the Neural Network for Nonlinear Hawkes processes (NNNH), a non-parametric method based on neural networks to fit nonlinear Hawkes processes. Our method is suitable for analyzing large datasets in which events exhibit…
Hawkes processes have recently risen to the forefront of tools when it comes to modeling and generating sequential events data. Multidimensional Hawkes processes model both the self and cross-excitation between different types of events and…
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…
In this paper, we study law of large numbers, central limit theorem, large and moderate deviations for INAR($\infty$) processes, which as a special case, includes both discrete-time linear Hawkes process and INAR(1) process in the…
We analyze the probability density function (PDF) of waiting times between financial loss exceedances. The empirical PDFs are fitted with the self-excited Hawkes conditional Poisson process with a long power law memory kernel. The Hawkes…
We consider a population of $N$ interacting neurons, represented by a multivariate Hawkes process: the firing rate of each neuron depends on the history of the connected neurons. Contrary to the mean-field framework where the interaction…
We investigate spatio-temporal event analysis using point processes. Inferring the dynamics of event sequences spatiotemporally has many practical applications including crime prediction, social media analysis, and traffic forecasting. In…
We prove a law of large numbers and a functional central limit theorem for multivariate Hawkes processes observed over a time interval $[0,T]$ in the limit $T \rightarrow \infty$. We further exhibit the asymptotic behaviour of the…
In this paper we prove scalar and sample path large deviation principles for a large class of Poisson cluster processes. As a consequence, we provide a large deviation principle for ergodic Hawkes point processes.
In this paper, we investigate the asymptotic behavior of nearly unstable Hawkes processes whose regression kernel has $L^1$ norm strictly greater than one and close to one as time goes to infinity. We find that,the scaling size determines…
Self- and mutually-exciting point processes are popular models in machine learning and statistics for dependent discrete event data. To date, most existing models assume stationary kernels (including the classical Hawkes processes) and…
We study the continuous time limit of a self-exciting negative binomial process and discuss the critical properties of its intensity distribution. In this limit, the process transforms into a marked Hawkes process. The probability mass…
In the last decade Hawkes processes have received much attention as models for functional connectivity in neural spiking networks and other dynamical systems with a cascade behavior. In this paper we establish a renewal approach for…
This paper investigates the asymptotic behavior of suitably time-modulated Hawkes processes with heavy-tailed kernels in a nearly unstable regime. We show that, under appropriate scaling, both the intensity processes and the rescaled Hawkes…
Some recent papers relate the criticality of complex systems to their maximal capacity of information processing. In the present paper, we consider high dimensional point processes, known as age-dependent Hawkes processes, which have been…
This paper considers population processes in which general, not necessarily Markovian, multivariate Hawkes processes dictate the stochastic arrivals. We establish results to determine the corresponding time-dependent joint probability…
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…
Hawkes process is one of the most commonly used models for investigating the self-exciting nature of earthquake occurrences. However, seismicity patterns have complicated characteristics due to heterogeneous geology and stresses, for which…
Price changes are induced by aggressive market orders in stock market. We introduce a bivariate marked Hawkes process to model aggressive market order arrivals at the microstructural level. The order arrival intensity is marked by an…