Related papers: Functional approximation of the marked Hawkes risk…

In this paper, we establish a large deviations principle for a multivariate compound process induced by a multivariate Hawkes process with random marks. Our proof hinges on showing essential smoothness of the limiting cumulant of the…

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…

Across a wide variety of applications, the self-exciting Hawkes process has been used to model phenomena in which the history of events influences future occurrences. However, there may be many situations in which the past events only…

The Hawkes process is a widely used model in many areas, such as finance, seismology, neuroscience, epidemiology, and social sciences. Estimation of the Hawkes process from continuous observations of a sample path is relatively…

This paper provides convergence analysis for the approximation of a class of path-dependent functionals underlying a continuous stochastic process. In the first part, given a sequence of weak convergent processes, we provide a sufficient…

In this paper, we study precise deviations including precise large deviations and moderate deviations for discrete marked Hawkes processes for large time asymptotics by using mod-$\phi$ convergence theory.

We give a construction of the Hawkes process as a piecewise competing risks model. We argue that the most natural interpretation of the self-excitation kernel is the hazard function of a defective random variable. This establishes a link…

Traditionally, Hawkes processes are used to model time--continuous point processes with history dependence. Here we propose an extended model where the self--effects are of both excitatory and inhibitory type and follow a Gaussian Process.…

Many events occur in the world. Some event types are stochastically excited or inhibited---in the sense of having their probabilities elevated or decreased---by patterns in the sequence of previous events. Discovering such patterns can help…

We propose a discrete time discrete space Markov chain approximation with a Brownian bridge correction for computing curvilinear boundary crossing probabilities of a general diffusion process on a finite time interval. For broad classes of…

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…

Critically ill patients in regular wards are vulnerable to unanticipated adverse events which require prompt transfer to the intensive care unit (ICU). To allow for accurate prognosis of deteriorating patients, we develop a novel…

In this paper, a framework on a discrete observation of (marked) point processes under the high-frequency observation is developed. Based on this framework, we first clarify the relation between random coefficient integer-valued…

The Hawkes process is a simple point process, whose intensity function depends on the entire past history and is self-exciting and has the clustering property. The Hawkes process is in general non-Markovian. The linear Hawkes process has…

We propose a fast and efficient estimation method that is able to accurately recover the parameters of a d-dimensional Hawkes point-process from a set of observations. We exploit a mean-field approximation that is valid when the…

We consider a discrete-time version of a Hawkes process defined as a Poisson auto-regressive process whose parameters depend on the past of the trajectory. We allow these parameters to take on negative values, modelling inhibition. More…

We present a Markov approximation for jump-diffusions whose jump part consists in a Hawkes process with intensity driven by a general (possibly non-monotone) kernel. Under minimal integrability conditions, the kernel can be approximated by…

Reinforcement Learning Algorithms are predominantly developed for stationary environments, and the limited literature that considers nonstationary environments often involves specific assumptions about changes that can occur in transition…

Inspired by a duration-dependent life insurance model, we consider continuous-time semi-Markov jump processes, initially assumed to have a finite state-space. We develop approximations using jump processes that are time-homogeneous Markov,…

Temporal networks are characterised by interdependent link events between nodes, forming ordered sequences of links that may represent specific information flows in the system. Nevertheless, representing temporal networks using discrete…