Related papers: Nonlinear Hawkes Processes in Time-Varying System
Hawkes (1971) introduced a powerful multivariate point process model of mutually exciting processes to explain causal structure in data. In this paper it is shown that the Granger causality structure of such processes is fully encoded in…
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…
Generalized evolutionary point processes offer a class of point process models that allows for either excitation or inhibition based upon the history of the process. In this regard, we propose modeling which comprises generalization of the…
The process algebra HYPE was recently proposed as a fine-grained modelling approach for capturing the behaviour of hybrid systems. In the original proposal, each flow or influence affecting a variable is modelled separately and the overall…
Temporal networks allow representing connections between objects while incorporating the temporal dimension. While static network models can capture unchanging topological regularities, they often fail to model the effects associated with…
Dynamic heterogeneity has often been modeled by assuming that a single-particle observable, fluctuating at a molecular scale, is influenced by its coupling to environmental variables fluctuating on a second, perhaps slower, time scale.…
We propose a mean-field model of interacting point processes where each process has a memory of the time elapsed since its last event (age) and its recent past (leaky memory), generalizing Age-dependent Hawkes processes. The model is…
We construct flexible likelihoods for multi-output Gaussian process models that leverage neural networks as components. We make use of sparse variational inference methods to enable scalable approximate inference for the resulting class of…
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…
The aim of this paper is to provide a new method for the detection of either favored or avoided distances between genomic events along DNA sequences. These events are modeled by a Hawkes process. The biological problem is actually complex…
The present paper provides exact mathematical expressions for the high-order moments of spiking activity in a recurrently-connected network of linear Hawkes processes. It extends previous studies that have explored the case of a (linear)…
A multivariate Hawkes process enables self- and cross-excitations through a triggering matrix that behaves like an asymmetrical covariance structure, characterizing pairwise interactions between the event types. Full-rank estimation of all…
This paper extends the existing fractional Hawkes process to better model mainshock-aftershock sequences of earthquakes. The fractional Hawkes process is a self-exciting point process model with temporal decay kernel being a Mittag-Leffler…
We prove regenerative properties for the linear Hawkes process under minimal assumptions on the transfer function, which may have unbounded support. These results are applicable to sliding window statistical estimators. We exploit…
Multi-state models are frequently applied for representing processes evolving through a discrete set of state. Important classes of multi-state models arise when transitions between states may depend on the time since entry into the current…
The order flow in high-frequency financial markets has been of particular research interest in recent years, as it provides insights into trading and order execution strategies and leads to better understanding of the supply-demand…
Modeling event dynamics is central to many disciplines. Patterns in observed event arrival times are commonly modeled using point processes. Such event arrival data often exhibits self-exciting, heterogeneous and sporadic trends, which is…
Several methods have been developed for the simulation of the Hawkes process. The oldest approach is the inverse sampling transform (ITS) suggested in \citep{ozaki1979maximum}, but rapidly abandoned in favor of more efficient alternatives.…
Given a stationary point process, an intensity burst is defined as a short time period during which the number of counts is larger than the typical count rate. It might signal a local non-stationarity or the presence of an external…
This chapter first presents a rather personal view of some different aspects of predictability, going in crescendo from simple linear systems to high-dimensional nonlinear systems with stochastic forcing, which exhibit emergent properties…