Related papers: Efficient Simulation of Hawkes Processes using the…

We propose a fast and efficient estimation method that is able to accurately recover the parameters of a d-dimensional Hawkes point-process from a set of observations. We exploit a mean-field approximation that is valid when the…

In this paper we introduce a new model named CARMA(p,q)-Hawkes process as the Hawkes model with exponential kernel implies a strictly decreasing behaviour of the autocorrelation function and empirically evidences reject the monotonicity…

We study a class of interacting nonlinear Hawkes point processes on the integer lattice in which each component is reset after its own jumps. The intensity of a component depends on the post-reset activity of its nearest neighbours, which…

Existing spatio-temporal Hawkes process models typically rely on either parametric or semiparametric assumptions, limiting the model's ability to capture complex endogenous and exogenous event dynamics. We propose a fully Bayesian…

The main focus of this paper is to approximate time series data based on the closed-loop Volterra series representation. Volterra series expansions are a valuable tool for representing, analyzing, and synthesizing nonlinear dynamical…

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…

We propose an extension to Hawkes processes by treating the levels of self-excitation as a stochastic differential equation. Our new point process allows better approximation in application domains where events and intensities accelerate…

A key difficulty that arises from real event data is imprecision in the recording of event time-stamps. In many cases, retaining event times with a high precision is expensive due to the sheer volume of activity. Combined with practical…

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…

We introduce a simple, efficient and accurate nonnegative preserving numerical scheme for simulating the square-root process. The novel idea is to simulate the integrated square-root process first instead of the square-root process itself.…

The lifted Heston model is a stochastic volatility model emerging as a Markovian lift of the rough Heston model and the class of rough volatility processes. The model encodes the path dependency of volatility on a set of N square-root state…

We show that the jumps correlation matrix of a multivariate Hawkes process is related to the Hawkes kernel matrix through a system of Wiener-Hopf integral equations. A Wiener-Hopf argument allows one to prove that this system (in which the…

We prove a functional limit theorem for a pair of nearly unstable Hawkes processes coupled through a triangular cross-excitation mechanism, when the two kernels have distinct heavy-tail exponents. This heterogeneous regime produces two…

Spatio-temporal Hawkes point processes are a particularly interesting class of stochastic point processes for modeling self-exciting behavior, in which the occurrence of one event increases the probability of other events occurring. These…

We study an extension of the Heston stochastic volatility model that incorporates rough volatility and jump clustering phenomena. In our model, named the rough Hawkes Heston stochastic volatility model, the spot variance is a rough…

Hawkes processes are a self-exciting stochastic process used to describe phenomena whereby past events increase the probability of the occurrence of future events. This work presents a flexible approach for modelling a variant of these,…

The stationarity is assumed in vanilla Hawkes process, which reduces the model complexity but introduces a strong assumption. In this paper, we propose a fast multi-resolution segmentation algorithm to capture the time-varying…

The event sequence of many diverse systems is represented as a sequence of discrete events in a continuous space. Examples of such an event sequence are earthquake aftershock events, financial transactions, e-commerce transactions, social…

We study a compound Poisson (random time-change) approximation for stochastic differential equations (SDEs) and stochastic Volterra equations whose coefficients may be merely measurable in time and may even exhibit integrable singularities.…

For the simulations of unsteady flow, the global time step becomes really small with a large variation of local cell size. In this paper, an implicit high-order gas-kinetic scheme (HGKS) is developed to remove the restrictions on the time…