Related papers: A Fractional Model for Earthquakes

We analyze the space-time patterns of earthquake occurrence in southern California using a new method that treats earthquakes as a phase dynamical system. The system state vector is used to obtain a probability measure for current and…

It is useful to consider the earthquakes in terms of catastrophe theory. In the paper, we illustrate this statement by analysis foreshocks preceding the strong earthquakes. We focused on the so-called catastrophe flags, and on the triggers…

A theoretical analysis of the earthquake prediction problem in space-time is presented. We find an explicit structure of the optimal strategy and its relation to the generalized error diagram. This study is a generalization of the…

This paper is devoted to establishing the full scaling limit theorems for multivariate Hawkes processes. Under some mild conditions on the exciting kernels, we develop a new way to prove that after a suitable time-spatial scaling, the…

Event-driven systems in fields such as neuroscience, social networks, and finance often exhibit dynamics influenced by continuously evolving external covariates. Motivated by these applications, we introduce a new class of multivariate…

Multivariate Hawkes Processes (MHPs) are a class of point processes that can account for complex temporal dynamics among event sequences. In this work, we study the accuracy and computational efficiency of three classes of algorithms which,…

Aggressive behavior in autistic inpatient youth often arises in temporally clustered bursts complicating efforts to distinguish external triggers from internal escalation. The sample population branching factor-the expected number of new…

Models for forecasting earthquakes are currently tested prospectively in well-organized testing centers, using data collected after the models and their parameters are completely specified. The extent to which these models agree with the…

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…

Terrorist activities often exhibit temporal and spatial clustering, making the multivariate Hawkes process (MHP) a useful statistical model for analysing terrorism across different geographic regions. However, terror attack data from the…

We provide some theoretical extensions and a calibration protocol for our former dynamic optimal execution model. The Hawkes parameters and the propagator are estimated independently on financial data from stocks of the CAC40.…

Numerical models are starting to be used for determining the future behaviour of seismic faults and fault networks. Their final goal would be to forecast future large earthquakes. In order to use them for this task, it is necessary to…

Simple models for ruptures along a heterogeneous earthquake fault zone are studied, focussing on the interplay between the roles of disorder and dynamical effects. A class of models are found to operate naturally at a critical point whose…

Reading is a process that unfolds across space and time, alternating between fixations where a reader focuses on a specific point in space, and saccades where a reader rapidly shifts their focus to a new point. An ansatz of…

An extension of the Hawkes process, the Marked Hawkes process distinguishes itself by featuring variable jump size across each event, in contrast to the constant jump size observed in a Hawkes process without marks. While extensive…

Several recent works point out that the crowd of small unobservable earthquakes (with magnitudes below the detection threshold $m_d$) may play a significant and perhaps dominant role in triggering future seismicity. Using the ETAS branching…

If we assume that earthquakes are chaotic, and influenced locally then chaos theory suggests that there should be a temporal association between earthquakes in a local region that should be revealed with statistical examination. To date no…

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 hyperbolic partial differential equations (PDEs) for a dynamic description of the traffic behavior in road networks. These equations are coupled to a Hawkes process that models traffic accidents taking into account their…

Multivariate Hawkes processes are commonly used to model streaming networked event data in a wide variety of applications. However, it remains a challenge to extract reliable inference from complex datasets with uncertainty quantification.…