Related papers: Large deviations for Markovian nonlinear Hawkes pr…
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…
Spatio-temporal Hawkes point processes are a particularly interesting class of stochastic point processes for modeling self-exciting behavior, in which the occurrence of one event increases the probability of other events occurring. These…
We introduce a Markovian single point process model, with random intensity regulated through a buffer mechanism and a self-exciting effect controlling the arrival stream to the buffer. The model applies the principle of the Hawkes process…
We formulate the large deviations for a class of two scale chemical kinetic processes motivated from biological applications. The result is successfully applied to treat a genetic switching model with positive feedbacks. The corresponding…
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…
The marked Hawkes risk process is a compound point process for which the occurrence and amplitude of past events impact the future. Thanks to its autoregressive properties, it found applications in various fields such as neuosciences,…
In this paper, we introduce a new class of processes which are diffusions with jumps driven by a multivariate nonlinear Hawkes process. Our goal is to study their long-time behavior. In the case of exponential memory kernels for the…
We prove the large deviation principle for the trajectory of a broad class of mean field interacting Markov jump processes via a general analytic approach based on viscosity solutions. Examples include generalized Ehrenfest models as well…
We introduce a multivariate Hawkes process with constraints on its conditional density. It is a multivariate point process with conditional intensity similar to that of a multivariate Hawkes process but certain events are forbidden with…
We consider a two-dimensional Hamiltonian system perturbed by a small diffusion term, whose coefficient is state-dependent and non-degenerate. As a result, the process consists of the fast motion along the level curves and slow motion…
The Large Deviation Principle is established for stochastic models defined by past-dependent non linear recursions with small noise. In the Markov case we use the result to obtain an explicit expression for the asymptotics of exit time.
The Hawkes process, a self-exciting point process, has a wide range of applications in modeling earthquakes, social networks and stock markets. The established estimation process requires that researchers have access to the exact time…
Hawkes processes are a special class of temporal point processes which exhibit a natural notion of causality, as occurrence of events in the past may increase the probability of events in the future. Discovery of the underlying influence…
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…
We study the tail asymptotics of two functionals (the maximum and the sum of the marks) of a generic cluster in two sub-models of the marked Poisson cluster process, namely the renewal Poisson cluster process and the Hawkes process. Under…
In the present work, we introduce a general class of mean-field interacting nonlinear Hawkes processes modelling the reciprocal interactions between two neuronal populations, one excitatory and one inhibitory. The model incorporates two…
We present a careful analysis of possible issues on the application of the self-excited Hawkes process to high-frequency financial data. We carefully analyze a set of effects leading to significant biases in the estimation of the…
In this paper, we propose a stochastic process, which is a Cox-Ingersoll-Ross process with Hawkes jumps. It can be seen as a generalization of the classical Cox-Ingersoll-Ross process and the classical Hawkes process with exponential…
We examine a distributional fixed-point equation related to a multi-type branching process that is key in the cluster sizes analysis of multivariate heavy-tailed Hawkes processes. Specifically, we explore the tail behavior of its solution…
We generalize multivariate Hawkes processes mainly by including a dependence with respect to the age of the process, i.e. the delay since the last point. Within this class, we investigate the limit behaviour, when n goes to infinity, of a…