相关论文: Conditional Uniformity and Hawkes Processes

We introduce the Hawkes process with renewal immigration and make its statistical estimation possible with two Expectation Maximization (EM) algorithms. The standard Hawkes process introduces immigrant points via a Poisson process, and each…

A cluster representation for a Hawkes process with renewal immigration is obtained. The centre and satellite processes are indicated as a renewal process and generalized branching processes respectively. It is confirmed that the proposed…

The Hawkes process is a counting process that has self- and mutually-exciting features with many applications in various fields. In recent years, there have been many interests in the mean-field results of the Hawkes process and its…

In this paper, we develop an efficient nonparametric Bayesian estimation of the kernel function of Hawkes processes. The non-parametric Bayesian approach is important because it provides flexible Hawkes kernels and quantifies their…

This work introduces a self and mutually exciting point process that embeds flexible residuals and intensity with discretely Markovian dynamics. By allowing the integration of diverse residual distributions, this model serves as an…

We obtain quenched hitting distributions to be compound Poissonian for a certain class of random dynamical systems. The theory is general and designed to accommodate non-uniformly expanding behavior and targets that do not overlap much with…

It is often assumed that events cannot occur simultaneously when modelling data with point processes. This raises a problem as real-world data often contains synchronous observations due to aggregation or rounding, resulting from…

High-dimensional self-exciting point processes have been widely used in many application areas to model discrete event data in which past and current events affect the likelihood of future events. In this paper, we are concerned with…

We study the Stokes phenomenon via hyperfunctions for the solutions of the 1-dimensional complex heat equation under the condition that the Cauchy data are holomorphic on $\mathbb{C}$ but a finitely many singular or branching points with…

We prove a central limit type theorem for critical marked Hawkes processes. We study the case where the marks are i.i.d. with nonnegative values and their common distribution is either heavy tailed or has finite variance. The kernel…

Hawkes processes are often applied to model dependence and interaction phenomena in multivariate event data sets, such as neuronal spike trains, social interactions, and financial transactions. In the nonparametric setting, learning the…

We establish sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the Q-process, the process…

The origin(s) of the ubiquity of probability distribution functions (PDF) with power law tails is still a matter of fascination and investigation in many scientific fields from linguistic, social, economic, computer sciences to essentially…

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…

It has been recently found that a number of systems displaying crackling noise also show a remarkable behavior regarding the temporal occurrence of successive events versus their size: a scaling law for the probability distributions 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…

We prove a law of large numbers and functional central limit theorem for a class of multivariate Hawkes processes with time-dependent reproduction rate. We address the difficulties induced by the use of non-convolutive Volterra processes by…

We consider discrete time dynamical systems and show the link between Hitting Time Statistics (the distribution of the first time points land in asymptotically small sets) and Extreme Value Theory (distribution properties of the partial…

A validated simulation model primarily requires performing an appropriate input analysis mainly by determining the behavior of real-world processes using probability distributions. In many practical cases, probability distributions of the…

This article introduces autocorrelograms for time series of point processes. Such time series usually arise when a longer temporal or spatio-temporal point process is sliced into smaller time units; for example, when an annual process is…