Related papers: Hawkes process with tempered Mittag-Leffler kernel
We introduce a model-independent approximation for the branching ratio of Hawkes self-exciting point processes. Our estimator requires knowing only the mean and variance of the event count in a sufficiently large time window, statistics…
We study a class of Gaussian processes for which the posterior mean, for a particular choice of data, replicates a truncated Taylor expansion of any order. The data consist of derivative evaluations at the expansion point and the prior…
We estimate the general influence functions for spatio-temporal Hawkes processes using a tensor recovery approach by formulating the location dependent influence function that captures the influence of historical events as a tensor kernel.…
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…
Many event sequence data exhibit mutually exciting or inhibiting patterns. Reliable detection of such temporal dependency is crucial for scientific investigation. The de facto model is the Multivariate Hawkes Process (MHP), whose impact…
Let $F$ be a distribution function on $\mathbb{R}$ with $F(0) = 0 $ and density $f$. Let $\tilde{F}$ be the distribution function of $X_1 - X_2$, $X_i\sim F,\, i=1,2,\text{ iid}$. We show that for a critical Hawkes process with displacement…
Kernel density estimation on a finite interval poses an outstanding challenge because of the well-recognized bias at the boundaries of the interval. Motivated by an application in cancer research, we consider a boundary constraint linking…
A univariate Hawkes process is a simple point process that is self-exciting and has clustering effect. The intensity of this point process is given by the sum of a baseline intensity and another term that depends on the entire past history…
This paper is concerned with combined inference for point processes on the real line observed in a broken interval. For such processes, the classic history-based approach cannot be used. Instead, we adapt tools from sequential spatial point…
Hawkes processes are point processes with self-exciting and clustering properties that are popular in applications. In recent years, renewal Hawkes processes have gained attention, due to their versatility such as the capability of…
This paper investigates the asymptotic behavior of suitably time-modulated Hawkes processes with heavy-tailed kernels in a nearly unstable regime. We show that, under appropriate scaling, both the intensity processes and the rescaled Hawkes…
Kernel-weighted test statistics have been widely used in a variety of settings including non-stationary regression, inference on propensity score and panel data models. We develop the limit theory for a kernel-based specification test of a…
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…
In this paper, we establish the asymptotic behavior of {\it supercritical} nearly unstable Hawkes processes with a power law kernel. We find that, the Hawkes process in our context admits a similar equation to that in \cite{MR3563196} for…
This paper studies by means of standard analytic tools the small time behavior of the heat content over a bounded Lebesgue measurable set of finite perimeter by working with the set covariance function and by imposing conditions on the heat…
We propose a new sparse Granger-causal learning framework for temporal event data. We focus on a specific class of point processes called the Hawkes process. We begin by pointing out that most of the existing sparse causal learning…
Sequential hypothesis testing is a desirable decision making strategy in any time sensitive scenario. Compared with fixed sample-size testing, sequential testing is capable of achieving identical probability of error requirements using less…
Refining one's hypotheses in the light of data is a common scientific practice; however, the dependency on the data introduces selection bias and can lead to specious statistical analysis. An approach for addressing this is via conditioning…
This study considers the Merton model with temporal correlation. We show the Merton model becomes Poisson process with the log-normal distributed intensity function in the limit. We discuss the relation between this model and Hawkes…
Obtaining reliable, adaptive confidence sets for prediction functions (hypotheses) is a central challenge in sequential decision-making tasks, such as bandits and model-based reinforcement learning. These confidence sets typically rely on…