Related papers: Renewal Hawkes Processes: Expectations and Applica…

We introduce, and formally establish, a variant of the Hawkes-fed birth-death process -- the delayed Hawkes birth-death process -- in which the conditional intensity does not increase at arrivals but at departures from the system. In a…

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…

We consider online monitoring of the network event data to detect local changes in a cluster when the affected data stream distribution shifts from one point process to another with different parameters. Specifically, we are interested in…

Multivariate Hawkes Processes (MHPs) are an important class of temporal point processes that have enabled key advances in understanding and predicting social information systems. However, due to their complex modeling of temporal…

Quadratic Hawkes (QHawkes) processes have proved effective at reproducing the statistics of price changes, capturing many of the stylised facts of financial markets. Motivated by the recently reported strong occurrence of endogenous…

We propose a simulation method for multidimensional Hawkes processes based on superposition theory of point processes. This formulation allows us to design efficient simulations for Hawkes processes with differing exponentially decaying…

This paper focuses on a class of linear Hawkes processes with general immigrants. These are counting processes with shot noise intensity, including self-excited and externally excited patterns. For such processes, we introduce the concept…

Multivariate Hawkes process provides a powerful framework for modeling temporal dependencies and event-driven interactions in complex systems. While existing methods primarily focus on uncovering causal structures among observed…

In this work, several convergence results are established for nearly critical self-excited systems in which event arrivals are described by multivariate marked Hawkes point processes. Under some mild high-frequency assumptions, the rescaled…

The fractional Poisson process has recently attracted experts from several fields of study. Its natural generalization of the ordinary Poisson process made the model more appealing for real-world applications. In this paper, we generalized…

We consider a sequential decision making problem where the agent faces the environment characterized by the stochastic discrete events and seeks an optimal intervention policy such that its long-term reward is maximized. This problem exists…

We study statistical aspects of state-dependent Hawkes processes, which are an extension of Hawkes processes where a self- and cross-exciting counting process and a state process are fully coupled, interacting with each other. The…

In this paper we provide an expansion formula for Hawkes processes which involves the addition of jumps at deterministic times to the Hawkes process in the spirit of the well-known integration by parts formula (or more precisely the Mecke…

We propose a novel framework for modeling multiple multivariate point processes, each with heterogeneous event types that share an underlying space and obey the same generative mechanism. Focusing on Hawkes processes and their variants that…

The contagion dynamics can emerge in social networks when repeated activation is allowed. An interesting example of this phenomenon is retweet cascades where users allow to re-share content posted by other people with public accounts. To…

In this paper, we discuss integer-valued autoregressive time series (INAR), Hawkes point processes, and their interrelationship. Besides presenting structural analogies, we derive a convergence theorem. More specifically, we generalize the…

Modelling and forecasting the occurrence of extreme events is especially difficult when the event process is nonstationary, with changes in both the rate at which extremes occur and the magnitude of the extremes when they occur. We approach…

In this paper, we are interested in linear prediction of a particular kind of stochastic process, namely a marked temporal point process. The observations are event times recorded on the real line, with marks attached to each event. We show…

Many modern spatio-temporal data sets, in sociology, epidemiology or seismology, for example, exhibit self-exciting characteristics, triggering and clustering behaviors both at the same time, that a suitable Hawkes space-time process can…

Hawkes processes have been shown to be efficient in modeling bursty sequences in a variety of applications, such as finance and social network activity analysis. Traditionally, these models parameterize each process independently and assume…