Related papers: Brillinger mixing of determinantal point processes…
A point process is said to be rigid if for any bounded domain in the phase space, the number of particles in the domain is almost surely determined by the restriction of the configuration to the complement of our bounded domain. The main…
Mixing of binary fluids by moving stirrers is a commonplace process in many industrial applications, where even modest improvements in mixing efficiency could translate into considerable power savings or enhanced product quality. We propose…
Properties of strong mixing have been established for the stationary linear Hawkes process in the univariate case, and can serve as a basis for statistical applications. In this paper, we provide the technical arguments needed to extend the…
Central limit theorems play an important role in the study of statistical inference for stochastic processes. However, when the nonparametric local polynomial threshold estimator, especially local linear case, is employed to estimate the…
A new type of dependent thinning for point processes in continuous space is proposed, which leverages the advantages of determinantal point processes defined on finite spaces and, as such, is particularly amenable to statistical, numerical,…
We establish finite-dimensional central limit theorems for local, additive, interaction functions of temporally evolving point processes. The dynamics are those of a spatial Poisson process on the flat torus with points subject to a…
In this note we consider non-stationary cluster point processes and we derive their conditional intensity, i.e. the intensity of the process given the locations of one or more events of the process. We then provide some approximations of…
In this article, recent results about point processes are used in sampling theory. Precisely, we define and study a new class of sampling designs: determinantal sampling designs. The law of such designs is known, and there exists a simple…
This paper addresses the problem of estimating drift parameter of the Ornstein - Uhlenbeck type process, driven by the sum of independent standard and fractional Brownian motions. The maximum likelihood estimator is shown to be consistent…
We obtain the empirical strong law of large numbers, empirical Glivenko-Cantelli theorem, central limit theorem, functional central limit theorem for various nonparametric Bayesian priors which include the Dirichlet process with general…
Stochastic gradient algorithms are more and more studied since they can deal efficiently and online with large samples in high dimensional spaces. In this paper, we first establish a Central Limit Theorem for these estimates as well as for…
We derive an integration by parts formula for functionals of determinantal processes on compact sets, completing the arguments of [4]. This is used to show the existence of a configuration-valued diffusion process which is non-colliding and…
We obtain results on both weak and almost sure asymptotic behaviour of power variations of a linear combination of independent Wiener process and fractional Brownian motion. These results are used to construct strongly consistent parameter…
We establish sufficient conditions for the asymptotic normality of kernel density estimators, applied to causal linear random fields. Our conditions on the coefficients of linear random fields are weaker than known results, although our…
Determinantal point processes (DPPs) are repulsive point processes where the interaction between points depends on the determinant of a positive-semi definite matrix. In this paper, we study the limiting process of L-ensembles based on…
The stationary asymptotic properties of the diffusion limit of a multi-type branching process with neutral mutations are studied. For the critical and subcritical processes the interesting limits are those of quasi-stationary distributions…
In this paper some general theory is presented for locally stationary processes based on the stationary approximation and the stationary derivative. Laws of large numbers, central limit theorems as well as deterministic and stochastic bias…
A general method is presented for deriving the limiting behavior of estimators that are defined as the values of parameters optimizing an empirical criterion function. The asymptotic behavior of such estimators is typically deduced from…
Special case of a Gibbsian facet process on a fixed window with a discrete orientation distribution and with increasing intensity of the underlying Poisson process is studied. All asymptotic moments for interaction U-statistics are…
In this paper, we develop necessary and sufficient conditions for the validity of a martingale approximation for the partial sums of a stationary process in terms of the maximum of consecutive errors. Such an approximation is useful for…