Related papers: Statistical Inference for Ergodic Point Processes …
A piecewise-deterministic Markov process, specified by random jumps and switching semi-flows, as well as the associated Markov chain given by its post-jump locations, are investigated in this paper. The existence of an exponentially…
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…
We introduce a Markovian single point process model, with random intensity regulated through a buffer mechanism and a self-exciting effect controlling the arrival stream to the buffer. The model applies the principle of the Hawkes process…
We study the long-time behavior of an additive functional that takes into account the jumps of a symmetric Markov process. This process is assumed to be observed through a biased observation scheme that includes the survival to events of…
We provide probabilistic and computational results on Markovian multivariate Hawkes processes and induced population processes. By applying the Markov property, we characterize in closed form a joint transform, bijective to the probability…
Because of their tractability and their natural interpretations in term of market quantities, Hawkes processes are nowadays widely used in high-frequency finance. However, in practice, the statistical estimation results seem to show that…
This article provides an introduction to the asymptotic analysis of covariance parameter estimation for Gaussian processes. Maximum likelihood estimation is considered. The aim of this introduction is to be accessible to a wide audience and…
In this paper we survey the almost sure central limit theorem and its functional form (quenched) for stationary and ergodic processes. For additive functionals of a stationary and ergodic Markov chain these theorems are known under the…
Max-stable processes are widely used to model spatial extremes. These processes exhibit asymptotic dependence meaning that the large values of the process can occur simultaneously over space. Recently, inverted max-stable processes have…
This paper deals with the estimation problem of misspecified ergodic L\'evy driven stochastic differential equation models based on high-frequency samples. We utilize the widely applicable and tractable Gaussian quasi-likelihood approach…
In this article, we consider McKean stochastic differential equations, as well as their corresponding McKean-Vlasov partial differential equations, which admit a unique stationary state, and we study the linearized It\^o diffusion process…
In this paper we consider point processes specified on directed linear networks, i.e. linear networks with associated directions. We adapt the so-called conditional intensity function used for specifying point processes on the time line to…
Fueled in part by recent applications in neuroscience, the multivariate Hawkes process has become a popular tool for modeling the network of interactions among high-dimensional point process data. While evaluating the uncertainty of the…
For Markov processes with absorption, we provide general criteria ensuring the existence and the exponential non-uniform convergence in total variation norm to a quasi-stationary distribution. We also characterize a subset of its domain of…
This paper deals with ergodic theorems for particular time-inhomogeneous Markov processes, whose the time-inhomogeneity is asymptotically periodic. Under a Lyapunov/minorization condition, it is shown that, for any measurable bounded…
We consider a nonlinear multivariate Hawkes process having a variable length memory which allows to describe the activity of a neuronal network by its membrane potential. We propose a graphical construction of the process and we construct,…
Extreme value functionals of stochastic processes are inverse functionals of the first passage time -- a connection that renders their probability distribution functions equivalent. Here, we deepen this link and establish a framework for…
We give a generalization of the ergodic theorem for semi-Markov linear-type processes. This generalization is proved for the case when a common support of distributions defining this process is not arithmetic. Also we give an uniform…
Modelling and forecasting the occurrence of extreme events is especially difficult when the event process is nonstationary, with changes in both the rate at which extremes occur and the magnitude of the extremes when they occur. We approach…
We consider the problems of parameter estimation for several models of threshold ergodic diffusion processes in the asymptotics of large samples. These models are the direct continuous time analogues of the well-known in time series…