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Hawkes process is a class of simple point processes that is self-exciting and has clustering effect. The intensity of this point process depends on its entire past history. It has wide applications in finance, insurance, neuroscience,…

We consider the problem of learning the network of mutual excitations (i.e., the dependency graph) in a non-stationary, multivariate Hawkes process. We consider a general setting where baseline rates at each node are time-varying and delay…

Hawkes process provides an effective statistical framework for analyzing the time-dependent interaction of neuronal spiking activities. Although utilized in many real applications, the classic Hawkes process is incapable of modelling…

Learning the causal-interaction network of multivariate Hawkes processes is a useful task in many applications. Maximum-likelihood estimation is the most common approach to solve the problem in the presence of long observation sequences.…

The Hawkes process is a popular point process model for event sequences that exhibit temporal clustering. The intensity process of a Hawkes process consists of two components, the baseline intensity and the accumulated excitation effect due…

Harness engineering has emerged as an important inference-time technique for large language model (LLM) agents, aiming to improve long-term performance through task decomposition and guided execution. However, more elaborate harnesses are…

Tick-sizes not only influence the granularity of the price formation process but also affect market agents' behavior. We investigate the disparity in the microstructural properties of the Limit Order Book (LOB) across a basket of assets…

Many modern spatio-temporal data sets, in sociology, epidemiology or seismology, for example, exhibit self-exciting characteristics, triggering and clustering behaviors both at the same time, that a suitable Hawkes space-time process can…

Low-level database operators often admit multiple physical implementations ("kernels") that are semantically equivalent but have vastly different performance characteristics depending on the input data distribution. Existing database…

Detecting rare events, those defined to give rise to high impact but have a low probability of occurring, is a challenge in a number of domains including meteorological, environmental, financial and economic. The use of machine learning to…

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…

In this paper we consider some non linear Hawkes processes with signed reproduction function (or memory kernel) thus exhibiting both self-excitation and inhibition. We provide a Law of Large Numbers, a Central Limit Theorem and large…

Many self-exciting systems change because endogenous amplification, as opposed to exogenous forcing, varies. We study a Hawkes process with fixed background rate and kernel, but piecewise time-varying productivity. For exponential kernels…

There is a pervasive assumption that low latency access to an exchange is a key factor in the profitability of many high-frequency trading strategies. This belief is evidenced by the "arms race" undertaken by certain financial firms to…

We prove that the number of points of a stationary linear Hawkes process lying in any bounded subset of the real line has exponential moments, without any other assumption than the one needed for existence of such stationary process, namely…

We establish the weak convergence of the intensity of a nearly-unstable Hawkes process with heavy-tailed kernel. Our result is used to derive a scaling limit for a financial market model where orders to buy or sell an asset arrive according…

Hawkes processes have recently gained increasing attention from the machine learning community for their versatility in modeling event sequence data. While they have a rich history going back decades, some of their properties, such as…

Hawkes Processes are a type of point process which models self-excitement among time events. It has been used in a myriad of applications, ranging from finance and earthquakes to crime rates and social network activity analysis.Recently, a…

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…

In this paper, we study various new Hawkes processes. Specifically, we construct general compound Hawkes processes and investigate their properties in limit order books. With regards to these general compound Hawkes processes, we prove a…