Related papers: Mixing properties for multivariate Hawkes processe…
In this work we investigate the generic properties of a stochastic linear model in the regime of high-dimensionality. We consider in particular the Vector AutoRegressive model (VAR) and the multivariate Hawkes process. We analyze both…
In this work, we propose to catch the complexity of the membrane potential's dynamic of a motoneuron between its spikes, taking into account the spikes from other neurons around. Our approach relies on two types of data: extracellular…
We consider a positive recurrent one-dimensional diffusion process with continuous coefficients and we establish stable central limit theorems for a certain type of additive functionals of this diffusion. In other words we find some…
A Maxwell-Stefan system for fluid mixtures with driving forces depending on Cahn-Hilliard-type chemical potentials is analyzed. The corresponding parabolic cross-diffusion equations contain fourth-order derivatives and are considered in a…
We show that using only weak hyperbolicity (no smoothness, compactness or exponential rates) the Hopf argument produces multiple mixing in an elementary way. While this recovers classical results with far simpler proofs, the point is the…
We consider the long-term behaviour of critical multitype branching processes conditioned on non-extinction, both with respect to the forward and the ancestral processes. Forward in time, we prove a functional limit theorem in the space of…
We provide a framework for empirical process theory of locally stationary processes using the functional dependence measure. Our results extend known results for stationary Markov chains and mixing sequences by another common possibility to…
We study the asymptotic properties of the solutions of a nonlinear renewal equation. The main contribution of the present article is to provide stability and convergence results around equilibrium solutions, under some local subcritical…
We demonstrate that the correlations observed in conditioned multiplier distributions of the energy dissipation in fully developed turbulence can be understood as an unavoidable artefact of the observation procedure. Taking the latter into…
A point process for event arrivals in high frequency trading is presented. The intensity is the product of a Hawkes process and high dimensional functions of covariates derived from the order book. Conditions for stationarity of the process…
Multivariate Hawkes Processes (MHPs) are a class of point processes that can account for complex temporal dynamics among event sequences. In this work, we study the accuracy and computational efficiency of three classes of algorithms which,…
This paper considers functional central limit theorems for stationary absolutely regular mixing processes. Bounds for the entropy with bracketing are derived using recent results in Nickl and P\"otscher (2007). More specifically, their…
We derive strong mixing conditions for many existing discrete-valued time series models that include exogenous covariates in the dynamic. Our main contribution is to study how a mixing condition on the covariate process transfers to a…
Let $(U_n(t))_{t\in\R^d}$ be the empirical process associated to an $\R^d$-valued stationary process $(X_i)_{i\ge 0}$. We give general conditions, which only involve processes $(f(X_i))_{i\ge 0}$ for a restricted class of functions $f$,…
The extent to which a matching engine can cloud the modelling of underlying order submission and management processes in a financial market remains an unanswered concern with regards to market models. Here we consider a 10-variate Hawkes…
This note examines linear combinations of multi-indexed sequences and derives the multivariate generating function of such a linear combination in terms of the original sequence's m.g.f. Applications include finding distributions and…
In this paper we introduce the \textit{multivariate} Brownian semistationary (BSS) processes and study the joint asymptotic behaviour of its realised covariation using in-fill asymptotics. First, we present a central limit theorem for…
This paper presents an algorithm for the simulation of Hawkes-type processes where the intensity is expressed in terms of a continuous-time autoregressive moving average model. We identify upper bounds for both the univariate and the…
Let $X$ be a continuous-time strongly mixing or weakly dependent process and $T$ a renewal process independent of $X$ with inter-arrival times $\tau$. We show general conditions under which the sampled process $(X_{T_i},T_i-T_{i-1})^{\top}$…
We consider multi-class systems of interacting nonlinear Hawkes processes modeling several large families of neurons and study their mean field limits. As the total number of neurons goes to infinity we prove that the evolution within each…