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Events in an online social network can be categorized roughly into endogenous events, where users just respond to the actions of their neighbors within the network, or exogenous events, where users take actions due to drives external to the…
We develop a new family of marked point processes by focusing the characteristic properties of marked Hawkes processes exclusively to the space of marks, providing the freedom to specify a different model for the occurrence times. This is…
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…
We provide probabilistic and computational results on Markovian multivariate Hawkes processes and induced population processes. By applying the Markov property, we characterize in closed form a joint transform, bijective to the probability…
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…
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…
The global dynamics of event cascades are often governed by the local dynamics of peer influence. However, detecting social influence from observational data is challenging due to confounds like homophily and practical issues like missing…
The ability to understand and eventually predict the emergence of information and activation cascades in social networks is core to complex socio-technical systems research. However, the complexity of social interactions makes this a…
Information diffusion on social networks has been described as a collective outcome of threshold behaviors in the framework of threshold models. However, since the existing models do not take into account individuals' optimization problem,…
Online social networks play a major role in the spread of information at very large scale and it becomes essential to provide means to analyse this phenomenon. In this paper we address the issue of predicting the temporal dynamics of the…
We derive the mean-field equations characterizing the dynamics of a rumor process that takes place on top of complex heterogeneous networks. These equations are solved numerically by means of a stochastic approach. First, we present…
A simple Hawkes model have been developed for the price tick structure dynamics incorporating market microstructure noise and trade clustering. In this paper, the model is extended with random mark to deal with more realistic price tick…
In the presence of modeling errors, the mainstream Bayesian methods seldom give a realistic account of uncertainties as they commonly underestimate the inherent variability of parameters. This problem is not due to any misconception in the…
Over the past few decades, the Hawkes process has become a popular framework for modeling temporal events thanks to its flexibility to capture different dependency structures. The objective of this work is to model call sequences emitted by…
The massive amount of text data on the web has facilitated research on the quantitative analysis of public opinion, which could not be visualized earlier. In this paper, we propose a new opinion dynamics theory. This theory that is intended…
We propose a novel modeling framework for time-evolving networks allowing for long-term dependence in network features that update in continuous time. Dynamic network growth is functionally parameterized via the conditional intensity of a…
The monitoring of conflict risk in the humanitarian sector is largely based on simple historic averages. The overarching goal of this work is to assess the potential for using a more statistically rigorous approach to monitor the risk of…
The Hawkes model is a past-dependent point process, widely used in various fields for modeling temporal clustering of events. Extending this framework, the multidimensional marked Hawkes process incorporates multiple interacting event types…
An avalanche or cascade occurs when one event causes one or more subsequent events, which in turn may cause further events in a chain reaction. Avalanching dynamics are studied in many disciplines, with a recent focus on average avalanche…
We present a stability study of the class of multivariate self-excited Hawkes point processes, that can model natural and social systems, including earthquakes, epileptic seizures and the dynamics of neuron assemblies, bursts of exchanges…